Green Book (2002 BS8110)

Using the unfactored loads and moments, calculate the number of piles required under each column.

When using precast floors, the following considerations should be made:

1. Consider using a structural topping to reduce cracking risk, especially under heavy concentrated loads or moving loads.
2. Evaluate fire rating, durability, and acoustic insulation along with structural strength.
3. Ensure a minimum bearing of 75mm on concrete beams and walls; refer to BS 8110 if this cannot be achieved.
4. Account for cambers in prestressed precast components when applying finishes, especially if adjoining units have different spans.

A ceiling to mask steps between adjoining units is necessary to provide a smooth transition and aesthetic finish between different levels, enhancing the overall appearance and functionality of the space.

Holes required for services need to be planned in advance to ensure that they do not compromise the structural integrity and functionality of the building, allowing for proper installation of utilities without interference.

Dividing structural frames into sub-frames allows for a more manageable analysis of moments, loads, and shear forces, facilitating the design of individual columns and beams while ensuring structural integrity under vertical loads.

The criteria for redistributing moments include:

1. Equilibrium must be maintained for each load case.
2. The design redistributed moment at any section should not be less than 70% of the elastic moment.
3. The design moment for the columns should be the greater of the redistributed moment or the elastic moment prior to redistribution.

The loading conditions for elastic analysis should consider:

• All spans with maximum ultimate load (1.4Gk + 1.6Qk).
• Alternate spans with maximum ultimate load and all other spans with minimum ultimate loads (1.0Gk).

The maximum percentage of moment redistribution allowed in structural design is up to 30%, with 15% being a reasonable limit for practical applications.

Moment redistribution allows for the adjustment of moments in a continuous beam to optimize structural performance by reducing hogging moments at supports and increasing sagging moments in spans. This helps in achieving a more efficient load distribution and enhances the overall stability of the structure.

Shear calculations at the ultimate limit state should be based on shear forces that are compatible with the bending moments arising from the specified load combinations and any moment redistribution that has been performed according to the relevant clauses.

The area of tension reinforcement or compression reinforcement should not exceed *0.04 b_uh.

Main bars in beams should normally be not less than size 16.

Piles should be grouped symmetrically under the loads.

The load carried by each pile is equal to N divided by the number of piles.

The aims of the manual include providing guidance on the design and construction of reinforced concrete structures, ensuring safety, stability, and durability in structural design.

Stability is crucial in structural design as it ensures that structures can withstand loads and environmental conditions without collapsing or undergoing unacceptable deformations.

Factors in the initial design phase include loads, material properties, structural form and framing, fire resistance and durability, and stiffness.

The purpose of checking all information in the final design phase is to ensure accuracy and completeness of design data, which is essential for safe and effective construction.

Key considerations for fire resistance and durability in slab design include:

• Fire Resistance: Ensuring that slabs can withstand high temperatures and prevent structural failure during a fire.
• Durability: Designing slabs to resist environmental factors such as moisture, chemicals, and wear over time, ensuring longevity and structural integrity.

The differences between one-way and two-way spanning slabs include:

Factors influencing span/effective depth ratios in slab design include:

• Type of Slab: Different slab types (e.g., solid, ribbed, coffered) have varying effective depths.
• Load Conditions: The magnitude and type of loads applied to the slab affect the required depth.
• Material Properties: The strength and stiffness of the materials used in the slab influence the effective depth needed for stability.

Main considerations in the section design of solid slabs include:

1. Bending: Ensuring the slab can resist bending moments without failure.
2. Shear: Designing for shear forces to prevent shear failure.
3. Openings: Accounting for any openings in the slab that may affect structural integrity and load distribution.

The significance of slenderness in column design includes:

• Stability: Slender columns are more susceptible to buckling under load, requiring careful analysis.
• Load Capacity: The slenderness ratio affects the load-carrying capacity of the column, influencing design choices.
• Fire Resistance: Slender columns may require additional fire protection measures to ensure safety during a fire event.

Key considerations for slenderness in wall design include:

1. Aspect Ratio: The ratio of height to thickness affects stability.
2. Buckling: Slender walls are more susceptible to buckling under axial loads.
3. Material Properties: The strength and stiffness of materials influence slenderness effects.
4. Load Conditions: Different loading conditions can impact the slenderness ratio and overall performance.

1. Equilibrium must be maintained.
2. The redistributed design moment at any section should not be less than 70% of the elastic moment.

In the loading diagrams:

• w1 represents the load/unit area for flights.
• w2 represents the load/unit area for landings.

The maximum span/effective depth ratio for cantilever stairs is 7.

For spans in excess of 10m, the span/effective depth ratios should be multiplied by 10 (span in metres).

Non-suspended ground slabs are generally designed on an empirical basis. Attention to practical details, thermal and moisture movements, and careful planning of joints and reinforcement are essential.

There is normally no need to calculate shear stresses in staircases supported on beams or walls, but the shear around columns should be checked in a similar manner to the shear around columns in solid flat slab construction.

The modification factors in Table 37 adjust the span/effective depth ratios based on the steel stress (N/mm²) and the design ultimate moment (M) at midspan or for a cantilever at the support.

The maximum area for casting slabs in bays is 50m², with the longer dimension of the bay limited to 10m.

The minimum thickness required for basement walls is at least 300mm.

The face exposed to the earth must be considered to be in a moderate environment, unless the soil is aggressive, in which case BRE Digest 363 should be complied with.

A minimum vertical surcharge of 10kN/m² should be considered.

The minimum area of reinforcement in each direction of the wall should be 0.4% of the gross cross-sectional area.

The foundation or base slab should be designed as a strip footing.

The type of foundation, sizes, and provisional formation levels depend on the results of the ground investigation.

1. Evaluate results of ground investigation to decide on spread or piled foundations.

2. Examine existing and future levels around the structure, considering bearing strata and ground water levels to determine provisional formation levels.

3. Calculate loads and moments on individual foundations using partial safety factors and imposed loading reduction in BS 6399 where appropriate.

4. Recalculate loads and moments on individual foundations without partial safety factors, using imposed loading reduction in BS 6399; often dividing factored loads by 1.45 is sufficiently accurate.

5. Calculate plan areas of spread footings or number of piles needed to support each column or wall using unfactored loads.

6. Calculate depth required for each foundation and reinforcement using factored loads.

• Cover to all reinforcement should be 50mm.

• Minimum cement content for reinforced foundations should be 300kg/m³.

• Maximum water/cement ratio should be 0.60.

• Characteristic strength of concrete for reinforced bases and pile caps should be not less than 35N/mm².

• For unreinforced bases, fou = 20N/mm² may be used with a minimum cement content of 220kg/m³.

• Follow recommendations of BRE Digest no. 363 where sulphates are present in significant concentrations.

Pile caps should extend at least 150mm beyond the theoretical circumference of the piles.

The moment should be resisted either by ground beams or by the piles.

The normalized bending moment 'M/bh^2fcu' indicates the bending capacity of reinforced concrete columns relative to their dimensions and material properties, helping to assess their structural performance under combined loading conditions.

The ratio 'd/h' being 0.80 indicates the depth-to-height ratio of the column, which is important for determining the effective depth of the column for resisting bending moments and ensuring adequate structural performance.

In the graph, filled circles represent bars that are included in calculating the area of steel reinforcement (Asc), while open circles represent bars that are not included in this calculation, indicating their contribution to the column's load-bearing capacity.

The curves illustrate how the relationship between normalized axial load (N/bhfcu) and normalized bending moment (M/bh^2fcu) varies with different values of the ratio pfy/fcu. This indicates how the axial load capacity and bending moment capacity of the reinforced concrete section change based on the yield strength of the reinforcing bars relative to the concrete strength.

The arrangement shows which bars are included (solid circles) and not included (open circles) in the calculation of Asc, which is the area of steel reinforcement. This distinction is crucial for determining the effective reinforcement in the concrete section and its structural performance.

The value of d/h = 0.75 indicates the ratio of the effective depth (d) to the overall depth (h) of the concrete section. This ratio is important for ensuring adequate strength and ductility in the design, as it influences the moment capacity and the distribution of stresses within the section.

The graph shows the relationship between N/h²fcu (on the y-axis) and M/h³fcu (on the x-axis), with several curves representing different values of pfy/fcu. Each curve indicates how the values of N and M change relative to each other based on varying pfy/fcu ratios.

The parameter hs/h = 0.9 indicates the ratio of the height of the inner circle of reinforcement (hs) to the overall height of the column (h), which is crucial for determining the effective reinforcement distribution within the column.

The total area of reinforcement (Asc) is related to the parameter p by the formula p = 4Asc/πh². This relationship helps in calculating the reinforcement required for the column based on its height and the area of reinforcement.

The graph shows that as the ratio of bending moment to compressive strength times the cube of the section height (M/h³fcu) increases, the ratio of axial load to compressive strength (N/m²fcu) generally increases for higher values of the parameter pfy/fcu. The curve for pfy/fcu = 1.4 has the highest values of N/m²fcu for a given M/h³fcu.

The curves plotted for different values of pfy/fcu indicate that higher reinforcement ratios lead to higher axial load to compressive strength ratios (N/m²fcu) for a given bending moment to compressive strength times the cube of the section height (M/h³fcu). The curve for pfy/fcu = 1.4 shows the highest values, while the curve for pfy/fcu = 0.0 starts at the origin and peaks before decreasing back to zero.

The formulas provided are significant for calculating the total area of reinforcement (Asc), the reinforcement ratio (ρ), and the relationship between the diameter of the core reinforcement (hs) and the height of the column (h). These calculations are essential for understanding the structural performance of reinforced concrete columns.

The average rib moment in two-way ribbed slabs is estimated as:

w (lylx / 24) c kNm per rib

where c is the rib spacing in metres, and the longer span should not exceed 1.5 times the shorter span.

For coffered slabs on column supports, the average bending moment at midspan is assessed on a width equal to the rib spacing, and for the column strips, this moment is increased by 15%.

The formula for calculating tension reinforcement is:

As = M / (0.95fy x 0.8d)

where M is the design ultimate bending moment under ultimate load at the critical section, and d is the effective depth.

Compression reinforcement is required for a rectangular section if M > 0.15fcubd². The area of the compression steel is calculated using:

A's = (M - 0.15fcu bd²) / (0.95fy (d - d'))

where d' is the depth to its centroid, b is the width of the section, and d is its effective depth.

If for flanged sections, M > 0.4fcbthr (d - 0.5hr), the section should be redesigned. Here, b and h are the width and thickness of the flange, and hr should not be taken as more than 0.5d.

After calculating the areas of the main reinforcement in the members, it should be checked that the bars can be properly arranged to meet the design requirements.

In beams, the area should generally be provided by not less than 2 nor more than 8 bars.

The bar spacing in slabs should not be less than 150mm nor more than 300mm.

Factors influencing fire resistance in wall design include:

1. Material Selection: Use of fire-resistant materials such as concrete and masonry.
2. Thickness: Thicker walls generally provide better fire resistance.
3. Insulation: Incorporating fire-resistant insulation can enhance performance.
4. Design Configuration: The arrangement and detailing of walls can affect fire spread and resistance.

Design considerations for walls resisting in-plane moments and axial loads include:

1. Reinforcement Layout: Proper placement of reinforcement to handle bending and axial forces.
2. Section Properties: Ensuring the wall section has adequate strength and stiffness.
3. Boundary Conditions: Understanding how the wall is supported and connected to other structural elements.
4. Load Combinations: Evaluating the effects of different load scenarios on wall performance.

Key aspects of section design for staircases include:

1. Bending Moments: Calculating moments due to loads on the staircase.
2. Shear Forces: Assessing shear forces acting on the staircase sections.
3. Effective Depth: Determining the effective depth for adequate strength and serviceability.
4. Material Properties: Selecting appropriate concrete grades for durability and performance.

Common types of foundations used in construction include:

1. Spread Footings: Used for distributing loads over a large area.
2. Pad Footings: Individual footings for columns or walls.
3. Strip Footings: Continuous footings for load-bearing walls.
4. Pile Foundations: Deep foundations used in weak soil conditions.
5. Raft Foundations: A large slab supporting multiple columns and walls.

The document mentions the following types of footings:

1. Strip footings
2. Combined footings
3. Balanced footings
4. Rafts
5. Pile caps

Key considerations for reinforcement in pile caps include:

• Design of reinforcement to ensure structural integrity.
• Anchorage and bond to connect the reinforcement effectively.
• Laps and splices to join reinforcement bars securely.
• Curtailment of reinforcement to optimize material use while maintaining strength.

Robustness in structural design is significant because it ensures:

• Structural integrity under unexpected loads or events.
• Tie forces and arrangements that help maintain stability.
• General safety and performance of the structure over its lifespan.

The detailing requirements for reinforcement include:

1. General detailing practices.
2. Bond and anchorage specifications.
3. Laps and splices for joining bars.
4. Hooks, bends, and bearings for proper reinforcement placement.
5. Curtailment of reinforcement to reduce material usage.
6. Corbels and nibs for additional support features.

K'factors are coefficients used to account for the effects of lateral-torsional buckling in beam design. They help in determining the effective length of the beam and its resistance to buckling under load.

The lever arm and neutral axis depth factors for beams are influenced by the beam's cross-sectional shape, the type of loading, and the material properties. These factors are crucial for calculating the moment capacity of the beam.

The minimum areas of tension reinforcement for beams are determined based on the beam's dimensions, the type of loading, and the material properties. This ensures adequate strength and ductility under service loads.

The clear distance between bars in beams is essential for ensuring proper concrete placement, bond strength, and preventing congestion. It is determined based on the percentage distribution of reinforcement to maintain structural integrity.

Ultimate shear stresses are critical in beam design as they determine the shear capacity of the beam. Understanding these stresses helps in designing adequate shear reinforcement to prevent shear failure.

Minimum provisions of links in beams are required to provide shear resistance and maintain the integrity of the beam under load. They help in controlling cracking and ensuring ductility.

The ultimate bending moments at the end support for simple one-way spanning slabs are 0.

Effective height factors for columns are used to account for the column's slenderness ratio and its susceptibility to buckling. These factors are crucial for determining the column's load-carrying capacity.

Fire resistance requirements for columns are established to ensure that they can withstand high temperatures during a fire event without losing structural integrity. This includes specific material and design considerations.

Durability requirements for columns involve considerations for environmental exposure, material selection, and protective measures to ensure long-term performance and resistance to deterioration.

Enhancement coefficients for biaxial bending are factors used to adjust the design strength of structural elements subjected to bending in two directions. They account for the interaction effects between the two bending moments.

Effective height factors for walls are important for assessing the wall's stability and load-carrying capacity, particularly in relation to buckling and lateral loads.

Fire resistance requirements for walls are designed to ensure that walls can withstand fire exposure for a specified duration, maintaining structural integrity and preventing fire spread.

Durability requirements for walls above ground focus on material selection, protective coatings, and design features that enhance resistance to weathering and environmental factors.

Span/effective depth ratios for stairs are used to ensure that the stairs can support the intended loads without excessive deflection or failure, contributing to safety and comfort.

Modification factors for M/bd² for stairs are used to adjust the design moment capacity based on the stair's geometry and loading conditions, ensuring adequate strength and stability.

Depth/projection ratios for unreinforced footings are critical for ensuring stability and load distribution, preventing excessive settlement or failure under load.

Reinforcement percentages, depth/projection ratios, and ground pressures for reinforced footings are essential for ensuring adequate load-bearing capacity and structural integrity, preventing failure due to soil settlement or lateral forces.

Ultimate anchorage bond lengths and lap lengths as multiples of bar size are critical for ensuring that reinforcement bars develop their full strength within the concrete, preventing bond failure.

Minimum radii, bend and hook sizes, and effective anchorage lengths are specified to ensure that reinforcement bars can be properly anchored and bent without compromising their strength or the concrete's integrity.

The Committee was formed to prepare a Manual for the design of reinforced concrete building structures compatible with British Standard BS 8110.

The Manual deliberately excludes prestressed and lightweight concretes, as well as structures that depend on the bending of columns for resistance against horizontal forces.

The initial design section is a novel feature of the Manual, providing guidance that aids in making a positive contribution to design practice.

The Manual aims for clarity and logical presentation of reinforced concrete design practice, with a concise format that is expected to be welcomed by users.

The two-way exchange during the preparation of the Manual has had an impact on BS 8110, indicating collaboration and feedback between the Manual's Committee and the BS 8110 Committee.

As a result of feedback from practising engineers, some span/depth values for initial design have been modified in the Manual.

The primary aim of the Manual is to provide guidance on the design of reinforced concrete building structures, ensuring compliance with BS 8110.

The Manual covers building structures using normal weight concrete that do not rely on bending in columns for resistance to horizontal forces.

One engineer should be responsible for the overall design, including stability, and ensure compatibility of the design and details of parts and components.

The structure should transmit dead, wind, and imposed loads directly to the foundations, ensuring a robust and stable structure that will not collapse progressively under misuse or accidental damage.

Floors must be able to act as horizontal diaphragms, especially if precast units are used, and should be designed to be structurally independent if divided by expansion joints.

All members of the structure should be effectively tied together in all directions, and elements whose failure could cause significant collapse should be avoided or strengthened with alternative load paths identified.

Movement joints minimize the effects of movement caused by shrinkage, temperature variations, creep, and settlement, and should divide the structure into individual sections.

Movement joints may be required where there is a significant change in the type of foundation or the height of the structure.

Horizontal forces should be distributed between the strongpoints according to their stiffness.

The 'adverse' and 'beneficial' factors should be used to produce the most onerous condition in load design.

For dead and imposed loads, the partial safety factors are:

Provided that the span/effective depth ratios and bar spacing rules are observed, it will not be necessary to check for serviceability limit states.

The partial safety factors for strength of materials, Ym, are the same as those given in BS 8110.

Initial design methods should be simple, quick, conservative, and reliable. Lengthy analytical methods should be avoided to facilitate the rapid production of viable schemes based on limited information.

Sizing of structural members should be based on the longest spans (for slabs and beams) and the largest areas of roof and/or floors carried (for beams, columns, walls, and foundations). Similar sizes should be assumed for less onerous cases to save design and costing time.

Simple structural schemes are quick to design and easy to build. They serve as a good 'benchmark' at the initial stage, allowing for potential complications later by other design team members without losing the foundational simplicity.

Loads should be based on relevant standards (BS 648, BS 6399, BS 8002). Imposed loading should initially use the highest statutory figures, and dead loading should be generous, with specific minimum values for different elements like floor finishes and partitions.

The design ultimate load is calculated as:

1. Dead load + Imposed load
2. 1.4 x characteristic dead load + 1.6 x characteristic imposed load

The combined effect can be calculated using either of the following formulas:

• 1.0 x characteristic dead load + 1.4 x characteristic wind load
• 1.4 x characteristic dead load + 1.4 x characteristic wind load

A characteristic concrete strength of 30N/mm² should be assumed for the initial design in normal construction in the UK.

The minimum column size should be 300 x 300mm or have an equivalent area.

To ensure stability against lateral forces, the following measures should be adopted:

1. Provide stability against lateral forces and ensure braced construction by arranging suitable shear walls symmetrically.
2. Adopt a simple arrangement of slabs, beams, and columns to carry loads to the foundations by the shortest routes.
3. Allow for movement joints.
4. Limit the span of slabs to 5-6m and beam spans to 8-10m on a regular grid; restrict column spacings to 8m for flat slabs.
5. Ensure robustness of the structure, especially if precast construction is used.

The size of structural members may be governed by the requirement of fire resistance and may also be affected by the cover necessary to ensure durability. For severe exposures, covers should be increased, and for simply supported members, sizes and covers should also be increased.

The depths of slabs should not be less than those derived from the specified ratios in the design guidelines, with specific ratios for two-way and one-way slabs based on the panel dimensions.

• Rib spacing should not exceed 900 mm.
• Rib width should not be less than 125 mm.
• Rib depth should not exceed four times its width.

The minimum structural topping thickness should preferably be 75 mm, but never less than 50 mm or one-tenth of the clear distance between ribs, whichever is greater.

To avoid excessive compression reinforcement and to ensure an economical amount of tension and shear reinforcement, facilitating the placing of concrete.

The effective depth ratios should be multiplied by 10 divided by the span in metres.

• Width of beams and ribs
• Column sizes and reinforcement
• Shear in flat slabs at columns
• Practicality of reinforcement arrangements in beams, slabs, and at beam-column junctions.

Ultimate loads, which are characteristic loads multiplied by the appropriate partial safety factors, should be used throughout.

The width should be determined by limiting the shear stress in beams to 2.0N/mm² and in ribs to 0.6N/mm² for concrete of characteristic strength fcu ≥ 30N/mm².

Width of beam (in mm) = 1000V/2d, where V is the maximum shear force (in kN) and d is the effective depth in mm.

The maximum ratio for stocky columns is 15, where the effective height equals 0.85 times the clear storey height.

The factor to multiply the ultimate load for such columns is 1.25.

It is recommended that the columns are made the same size through at least the two topmost storeys to avoid inadequate sizes due to large moments in relation to axial loads.

The ultimate loads are determined by dividing the total ultimate load, factored for eccentricities, by a 'stress' calculated as 0.35_fcu_ + p/100(0.67_fy_ - 0.35_fcu_), where fcu is the characteristic concrete strength, fy is the characteristic strength of reinforcement, and p is the percentage of reinforcement.

The shear force at the outer support for simple one-way spanning slabs is 0.4F.

Walls carrying vertical loads should be designed as columns, while shear walls should be designed as vertical cantilevers, with reinforcement arrangements checked as for a beam.

The maximum allowable shear stress is 0.6 N/mm², calculated using the formula: $\frac{1250w \text{ (area supported by column)} }{(\text{column perimeter}+9h) d} \leq 0.6 \text{N/mm}^2$ where w is the total ultimate load per unit area, d is the effective depth of the slab, h is the thickness of the slab, and areas are in m².

The second check states that the shear stress must satisfy: $\frac{1250w \text{ (area supported by column)} }{(\text{column perimeter}) d} \leq 0.8 \sqrt{f_{cu}} \text{ or } 5 \text{N/mm}^2 \text{, whichever is the lesser.}$

The conditions are:

1. The imposed load does not exceed the dead load.
2. There are at least three spans.
3. The spans do not differ in length by more than 15% of the longest span.

The average moment per metre width is calculated using the formula:

$w \frac{l_yl_x}{24} \text{ kNm per metre}$

where $l_y$ is the longer span and $l_x$ is the shorter span, with the condition that $l_y$ does not exceed 1.5 times $l_x$.

The moments per unit width in the column strips for solid flat slabs should be determined as 1.5 times those for one-way slabs.

For one-way ribbed slabs, the bending moments at midspan are assessed on a width equal to the rib spacing, assuming simple supports throughout.

General arrangement drawings should include sections through the entire structure and a brief statement of the principal design assumptions, such as imposed loadings, weights of finishes, fire ratings, and durability.

Bar reinforcement should be described separately by steel type (e.g., mild or high yield steel), size, weight, and divided according to element of structure (e.g., foundations, slabs, walls, columns) and bar shape (e.g., straight, bent, hooked, curved, links, stirrups, spacers).

Method I is the simplest, based on the type of structure and the volume of the reinforced concrete elements, with typical values such as 1 tonne of reinforcement per 10m³ for warehouses, 1 tonne per 13.5m³ for offices, and 1 tonne per 15.0m³ for residential buildings.

Method 2 involves using factors that convert the steel areas obtained from initial design calculations to weights, such as kg/m² or kg/m, with reference to tables provided in the appendix for various structural elements.

The advantages include:

1. Representativeness: The sketches are representative of the actual structure.
2. Detailing: They include the intended form of detailing and distribution of main and secondary reinforcement.
3. Allowance for Variations: An allowance for additional steel for variations and holes can be made by inspection.

The following items should be considered:

1. Laps and Starter Bars: Allowance for normal laps in both main and distribution bars, and for starter bars.
2. Architectural Features: Sufficient allowance for reinforcement required for non-structural features.
3. Contingency: A contingency of 10-15% should be added for changes and possible omissions.

The first step is to check all information to ensure that the initial design assumptions are still valid, including comments from the client and design team, and results from the ground investigation.

Ensure that no amendments have been made to the sizes and disposition of the shear walls and that any openings can be accommodated in the final design.

Check that the loading assumptions for dead and imposed loading, including floor finishes, ceilings, services, partitions, external wall thicknesses, and design wind loading, are still correct. Also consider loadings such as earthquake, accidental, constructional, or other temporary loadings.

Establish the fire resistance required for each part of the structure, the durability classifications that apply, and the mass of floors and walls required for sound insulation in consultation with other members of the design team.

It is crucial to decide on the type of foundation to be used in the final design and to consider any existing or future structures adjacent to the perimeter that may influence the foundation location and effects on the superstructure and adjacent buildings.

Establish which codes of practice and other design criteria are to be used in the final design.

Factors to consider include:

• Fire-resistance and durability requirements
• Availability of constituents for concrete mixes
• Specific requirements such as water-excluding concrete for basements

The design information data list compiles information from previous checks and discussions with stakeholders, ensuring all relevant data is organized and approved by the design team leader before final design commences.

Details to be added include:

1. Grid lines established in two mutually perpendicular directions.
2. Unique reference numbers for walls, columns, beams, and slabs.
3. Marking of loads to be carried by each slab, including the width and location of any special loads.

The logical sequence for final design calculations is:

1. Slabs
2. Structural frames
3. Beams
4. Columns
5. Walls
6. Staircases
7. Retaining walls, basements
8. Foundations
9. Robustness
10. Detailing

The first step is to complete the design of the slabs to determine the final loading for the design of the frame.

1. Check that the section complies with requirements for fire resistance.
2. Check that cover and concrete grade comply with requirements for durability.
3. Calculate bending moments and shear forces.
4. Make final check on span/depth ratios.
5. Calculate reinforcement.
6. For flat slabs, check shear around columns and calculate shear reinforcement if necessary.

Special precautions against spalling may be required, such as partial replacement by plaster, lightweight aggregate, or the use of fabric as supplementary reinforcement.

The cover may be decreased as follows:

• Increase in width of 25mm allows a decrease of 5mm in cover.
• Increase in width of 50mm allows a decrease of 10mm in cover.
• Increase in width of 100mm allows a decrease of 15mm in cover.
• Increase in width of 150mm allows a decrease of 15mm in cover.

The minimum overall depth is 95 mm and the cover to main reinforcement is 20 mm.

For a fire resistance of 1 hour, the minimum thickness/width is t/b 90/90. For 1.5 hours, it is 105/110; for 2 hours, 115/125; for 3 hours, 135/150; and for 4 hours, 150/175.

The key requirements for durability include:

1. An upper limit to the water/cement ratio
2. A lower limit to the cement content
3. A lower limit to the thickness of cover to the reinforcement
4. Good compaction
5. Adequate curing

Higher cement contents may be required to meet durability standards, but this can lead to increased shrinkage. Therefore, the potential problems of increased shrinkage should be considered in the design.

1. The area of each bay exceeds 30m².
2. The variation in the spans does not exceed 15% of the longest span.
3. The ratio of the characteristic imposed load to the characteristic dead load does not exceed 1.25.
4. The characteristic imposed load does not exceed 5kN/m², excluding partitions.
5. Elastic support moments other than at a cantilever support should be reduced by 20%, with a consequential increase in the span moments.
6. Equilibrium must be maintained and the redistributed moment at any section should not be less than 70% of the elastic moment.

The effective width of solid slabs is calculated using the formula:
Width = w + 2.4(1 - x/l)x
Where:

• w is the load width
• x is the distance to the nearer support from the section under consideration
• l is the span

Bending moments in two-way slabs may be calculated by:

1. Yield-line analysis.
2. Using coefficients for slabs with a long-to-short span ratio of 1.5 or less, defined as:
   • Msx = βsx wl²x
   • Msy = βsy wl²x where βsx and βsy are coefficients from Table 10 and lx is the shorter span.

The conditions in clause 4.2.3.1 must be met, and the coefficients provided in Table 9 should be used, which account for a 20% reduction in values.

A flat slab must have at least three spans in each direction, and the ratio of the longest span to the shortest must not exceed 1.2.

Bending moments in flat slabs should be obtained by frame analysis, considering the structure as divided into frames consisting of columns and strips of slab.

The bending moment coefficient for negative moments at continuous edges in interior panels for a short-span ratio of 1.0 is 0.031.

The bending moment coefficients for positive moments at midspan for interior panels are 0.024 at a short-span ratio of 1.0 and increase to 0.034 at a ratio of 1.25, and then to 0.045 at a ratio of 1.5.

The bending moment coefficient for positive moments at midspan for one short edge discontinuous panels with a short-span ratio of 1.0 is 0.029.

When one edge is discontinuous, the reactions on all continuous edges should be increased by 10%, and the reaction on the discontinuous edge may be reduced by 20%.

When adjacent edges are discontinuous, the reactions should be adjusted for elastic shear considering each span separately.

The ultimate bending moment at the first interior support for a simple slab connection is 0.086FI.

The shear force at the outer support for a continuous slab connection is 0.46F.

The total column moment at the first interior support for a simple slab connection is 0.04FI.

Flat slab panels are divided into column strips and middle strips. Drops should be ignored in the assessment of widths if their smaller dimension is less than one-third of the smaller dimension of the panel.

For negative moments, the division is as follows:

For positive moments, the division is as follows:

The maximum design moment is given by the formula:
M max = 0.15f cu be d²,
where d is the effective depth for the top reinforcement in the column strip.

The design moments of the half column strip adjacent to the beam or wall should be one-quarter of the design moments obtained from the analysis when the slab is supported by a wall or an edge beam with a depth greater than 1.5 times the thickness of the slab.

The design effective shear force Veff at the perimeter of internal columns with approximately equal spans is given by:
Veff = 1.15V,
where V is the design shear transferred to the column.

For internal columns with unequal spans, the effective shear force is calculated as:
Veff = Vt + 1.5M₁/x,
where x is the side of the column perimeter parallel to the axis of bending and M₁ is the design moment transmitted to the column.

Compliance with the span/effective depth ratios should generally limit total deflections to span/250.

The effective moment transfer strip 'be' is equal to 'Cx + y', where 'y' is the length of the slab from the column to the edge of the hole.

When the column is offset, the effective moment transfer strip 'be' is equal to 'Cx + y', where 'y' is the distance from the edge of the column to the right side of the effective moment transfer strip.

The effective moment transfer strip 'be' is equal to 'Cx + Cy', where 'Cx' is the width of the portion of the column outside of the slab and 'Cy' is the length of the portion of the column outside of the slab.

The effective moment transfer strip 'be' is equal to 'Cx + y/2', where 'y' is the distance from the edge of the column to the side of the effective moment transfer strip.

The effective moment transfer strip 'be' is equal to 'y/2 + x', where 'y' is the distance from the edge of the column to the side of the effective moment transfer strip, and 'x' is the distance from the edge of the column to the inner face.

The moment of resistance for concrete is given by the formula: Mu = K'fcu bd² where K' is obtained from the moment redistribution values.

For spans in excess of 10m, the span/effective depth ratios should be multiplied by 10/(span in metres).

The ratio of the longer span to the corresponding effective depth should not exceed the values for slabs on linear supports multiplied by 0.90.

The area of tension reinforcement is given by:

As = M/(0.95fy)z

where M is the moment, fy is the yield strength of the reinforcement, and z is the lever arm.

For two-way spanning slabs, care should be taken to use the value of d appropriate to the direction of the reinforcement.

The spacing of main bars should not exceed the lesser of:

1. 3d
2. 300mm
3. 70000β/pfy

where p is the reinforcement percentage and 0.3 < p < 1.0, and β is the ratio of moment after redistribution to moment before redistribution.

The spacing of distribution bars should not exceed the lesser of:

1. 3d
2. 400mm

The neutral axis depth x is defined as:

x = n.d

where n is a factor that varies based on the moment-to-depth ratio.

The minimum size for main bars in slabs should not be less than size 10.

The area of reinforcement in either direction should not be less than the greater of:

• one-quarter of the area of main reinforcement,
• 0.0013bh for high yield steel,
• 0.0024bh for mild steel,
• 0.0025bh for high yield steel or 0.003bh for mild steel if control of shrinkage and temperature cracking is critical, where h is the overall depth of the slab in mm.

At corners where the slab is not continuous, torsion reinforcement equal to three-quarters of the reinforcement in the shorter span should be provided in the top and bottom of the slab in each direction for a width in each direction of one-fifth of the shorter span.

Column and middle strips should be reinforced to withstand the design moments obtained from clause 4.2.3.4. Generally, two-thirds of the amount of reinforcement required to resist the negative design moment in the column strip should be placed in a width equal to half that of the column strip, symmetrically positioned about the centreline of the column.

The shear stress should be calculated using the formula v = 1000V/bwd, where V is the shear force, bw is the average width of the ribs, and d is the effective depth.

In the absence of heavy point loads, there is normally no need to calculate shear stresses in slabs on linear supports. However, for heavy point loads, the punching shear stress should be checked using the method for shear around columns in flat slabs.

The shear stress at the column perimeter is calculated using the formula: v = 1000Veff/Ucd N/mm², where Veff is the effective shear force in kN, d is the average effective depth in mm of both layers, and Uc is the column perimeter in mm.

The shear stress v must not exceed 0.8 √fou or 5 N/mm², whichever is the lesser.

The part of the perimeter that is enclosed by radial projections from the centroid of the column to the openings should be considered ineffective.

1. Check the shear stress at Perimeter (b).
2. If the shear stress is less than the permissible ultimate shear stress (ve), no further checks are required.
3. If v > ve, check successive perimeters until one is reached where v < ve.

Shear reinforcement could be provided where the slab thickness is at least 250mm.

Column heads or drop panels should be incorporated, or the slab thickness should be increased to reduce the shear to less than 2*ve.

Asv = (v - ve) * ud / (0.95 * fyv)

Asv = 5 * (0.7v - ve) * ud / (0.95 * fyv)

A sy should not be taken as less than 0.4 * ud / (0.95 * fyv).

The designated failure zones for punching shear reinforcement in a concrete slab are:

1. Failure Zone 1 - Located around the face of the loaded area or support, requiring at least two perimeters of reinforcement.
2. Failure Zone 2 - Also requires at least two perimeters of reinforcement, with the required area of reinforcement provided within this zone.

Reinforcement common to both failure zones may be utilized in both areas.

The effective depth range in Table 15 is from 150 mm to 400 mm.

Reinforcement should be provided on at least two perimeters: the first perimeter should be located approximately 0.5d from the face of the column area and should contain not less than 40% of A_sv. The second perimeter should be located at not more than 0.75d from the first.

For f_cu = 25N/mm², divide the values by 1.062; for f_cu = 35N/mm², multiply by 1.053; for f_cu = 40N/mm², multiply by 1.10.

The spacing of the legs of links around any perimeter should not exceed 1.5d.

The shear is checked on perimeter (c), and if reinforcement is required, it is provided between perimeters (a) and (c) in a manner analogous to the check on the critical perimeter.

Openings should be trimmed with special beams or reinforcement to ensure the designed strength is not unduly impaired. Additionally, the area of reinforcement interrupted by openings should be replaced by an equivalent amount, with half placed along each edge of the opening.

The bending moments per metre width for solid slabs should be multiplied by the spacing of the ribs to obtain the bending moments per rib.

The maximum span/effective depth ratio for cantilever ribbed slabs with bw/b=1 is 7.

For spans in excess of 10m, the ratios should be multiplied by 10 divided by the span in metres.

If the design shear stress v exceeds the permissible shear stress ve, one of the following actions should be adopted:

1. Increase width of rib
2. Reduce spacing of ribs
3. Provide solid concrete at supports
4. Provide shear reinforcement only if none of the above is possible.

Beam strips in ribbed and coffered slabs should be designed as follows:

• The slabs should be designed as continuous.
• The beam strips should be designed as beams spanning between the columns.
• The shear around the columns should be checked similarly to the shear around columns in solid flat slabs.

1. Check that the section complies with fire resistance requirements.

2. Check that cover and concrete comply with durability requirements.

3. Calculate bending moments and shear forces according to subsection 4.3 or clause 4.4.3(b).

4. Check span/depth ratio and determine the compression steel required to limit deflection.

5. Calculate reinforcement.

The effective span of a simply supported beam should be taken as the smaller of:

(a) The distance between the centres of bearings, or (b) The clear distance between supports plus the effective depth d of the beam.

The clear distance between adequate lateral restraints to a beam should not exceed the lesser of:

• 60b_c
• 250b_c^2/d

where b_c is the width of the compression flange midway between the restraints.

If the width of the beam is more than the minimum in Table 17, the cover may be decreased as follows:

Special precautions against spalling may be required, such as:

• Partial replacement by plaster
• Use of lightweight aggregate
• Use of fabric as supplementary reinforcement (see BS 8110, Part 2)

1. An upper limit to the water/cement ratio.
2. A lower limit to the cement content.
3. A lower limit to the thickness of the cover to the reinforcement.
4. Good compaction of the concrete.
5. Adequate curing of the concrete.

The maximum values can be obtained by:

1. Considering the beam as part of a structural frame.
2. Treating the beam as continuous over its supports, allowing free rotation about them.

Higher cement contents may lead to increased shrinkage. This potential problem should be considered during the design process.

The span/effective depth ratio should not exceed the value in Table 20 multiplied by the modification factor in Table 21 to ensure that total deflection does not exceed span/250.

The condition of maximum load on the cantilever and minimum load on the adjoining span must be checked.

The values are as follows:

M is to be taken as the moment at midspan, or for a cantilever at the support, which is crucial for determining the span/effective depth ratios and modification factors.

If the applied moment M is less than the resistance moment Mu, compression steel will not be needed in the design of the beam.

1. Calculate Ma for concrete using the formula: Ma = K'fubd², where K' is obtained from Table 23.

2. If M ≤ Ma for the concrete, calculate the area of tension reinforcement As using the formula: As = M / (0.95fy)z, where z is obtained from Table 24 for different values of K.

The lever arm z is obtained from Table 24 for different values of K, where K is defined as K = M/bd² fcu.

A's = (M - Mu) / (0.95fy (d - d')) where d' is the depth of the compression steel from the compression face.

As = (Mu / (0.95fy*z)) + A's

For T-beams, b is the web width plus 0.2lz or the actual flange width if less, where lz is the distance between points of zero moment.

For L-beams, b is the web width plus 0.1lz or the actual flange width if less, where lz is the distance between points of zero moment.

Check the position of the neutral axis by determining K = M / (fcu*bd^2) using flange width b and selecting values of n and z from Table 24. Calculate x = nd.

Muf = 0.45 * fcu * (b - bw) * hr * (d - 0.5 * hr)

If Kr ≤ K', select the value of a1 from Table 24 and calculate As. If Kr > K', redesign the section or consult BS 8110 for design of compression steel.

Minimum area = 0.0024 * b * h

Minimum area = 0.002 * bw * h

Minimum area = 0.002 * b * h

Minimum area = 0.0048 * b * h

Minimum area = 0.0015 * hi per metre width

Longitudinal bars should be provided at a spacing not exceeding 250mm. The size of the bars should be:

• 0.75√b_w for high yield bars (f_y = 460N/mm²)
• 100√b_w for mild steel bars (f_y = 250N/mm²)

The clear space between main bars should not exceed the values specified in Table 26 based on the percentage redistribution of the yield strength (f_y) of the bars.

The horizontal distance between bars should not be less than the bar size or the maximum size of the aggregate plus 5mm. The vertical distance between bars should not be less than:

• two-thirds the maximum size of the aggregate or
• when the bar size is greater than the maximum aggregate size plus 5mm, a spacing less than the bar size should be avoided.

The shear stress v at any point should be calculated using the formula:

v = (1000V)/(b_w d) N/mm²

The maximum allowable shear stress, v, should not exceed 0.8√𝑓𝑐𝑢 or 5 N/mm².

The ultimate shear stress, vc, decreases as the effective depth increases. For example, for 100As / bwd ≤ 0.15, the shear stress values range from 0.46 N/mm² at 150 mm to 0.36 N/mm² at 400 mm.

For different concrete strengths, the adjustments are as follows:

• For 𝑓𝑐𝑢 = 25 N/mm², divide by 1.062.
• For 𝑓𝑐𝑢 = 35 N/mm², multiply by 1.053.
• For 𝑓𝑐𝑢 = 40 N/mm², multiply by 1.10.

The maximum spacing of shear reinforcement links in the direction of the span should not exceed 0.75*d.

For compression reinforcement in an outer layer, every corner bar and alternate bar should be supported by a link passing around the bar with an included angle of not more than 135°. No bar within a compression zone should be further than 150 mm from a restrained bar.

Grade 250 (mild steel) links equal to 0.18% of the horizontal section throughout the beam, except in members of minor structural importance such as lintels.

The ratio of the effective height of a stocky column to its least cross-sectional dimension should be 15 or less. The effective height is obtained by multiplying the clear height between the lateral restraints at the two ends of the column by a specific factor.

1. Check that the column is not slender.
2. Check that section size and cover comply with requirements for fire resistance.
3. Check that cover and concrete comply with requirements for durability.
4. Calculate axial loads and moments according to subsection 4.5.3.
5. Design section and reinforcement.

The minimum dimension of a column should not be less than 200mm.

Small openings not exceeding 0.25d in diameter can be permitted within the middle third of the depths of beams, without detailed calculations, if the design shear stress is less than the permissible stress.

The requirements for durability include:

1. An upper limit to the water/cement ratio.
2. A lower limit to the cement content.
3. A lower limit to the thickness of the cover to the reinforcement.
4. Good compaction.
5. Adequate curing.

The minimum design moment for any column in any plane should be calculated by multiplying the ultimate design axial load by an eccentricity of 0.05 times the overall column dimension in the relevant plane, not exceeding 20mm.

1. Increase the loads obtained on the assumption that beams and slabs are simply supported by 10%.
2. A higher increase may be required for adjacent spans with grossly dissimilar loadings.

Moments in the columns may be obtained using subframes, subject to the minimum design moments specified.

1. Subframe on the left: Column fixed at both ends with a beam connected at the top, subjected to loads of 1.4GK + 1.6QK, with stiffness of 0.5Kb.

2. Subframe on the right: Similar column and beam setup, but the beam is subjected to a load of 1.0Gk, with two section stiffnesses of 0.5Kb1 and 0.5Kb2.

The formula for calculating the framing moment in the upper column (MFu) is:

MFu = Me * Ku / (KL + Ku + 0.5Kb)

The ultimate axial load capacity in N of the column is calculated using the formula:

Ultimate Axial Load Capacity = 0.4fcu * Ac + 0.8fy * Asc

Where:

• fcu = characteristic concrete cube strength in N/mm²
• Ac = area of concrete in mm²
• As = area of longitudinal reinforcement in mm²
• fy = characteristic strength of reinforcement in N/mm²

The ultimate axial load capacity of the column is given by:

Ultimate Axial Load Capacity = 0.35fcu * Ac + 0.7fy * Asc

Where the terms have the same definitions as in the previous formula.

When the moment about the x-x axis (Mx) is greater than or equal to the moment about the y-y axis (My), the increased moment about the x-x axis is calculated as Mx + β, where β is obtained from Table 32. If My is greater than Mx, the increased moment about the y-y axis is My + B.

The minimum area of reinforcement should be 0.4% of the gross cross-sectional area of concrete.

Longitudinal bars should not be less than size 12.

The enhancement coefficient β is determined from Table 32 based on the ratio of the design ultimate axial load (N) to the product of the dimensions b and h of the column.

The maximum area of reinforcement (other than at laps) should be 6% of the gross cross-sectional area of concrete, but 4% is generally preferable.

The maximum spacing of main bars should not exceed 250mm.

Links should be sized as the greater of one-quarter the size of the largest longitudinal bar or size 6. Every corner bar and each alternate bar in an outer layer should have a link passing around it, with an included angle not exceeding 135° except for hoops or spirals in circular columns.

The maximum spacing of links should be 12 times the size of the smallest compression bar but not more than the smallest cross-sectional dimension of the column.

The ratio of the effective height of stocky walls to their thickness should be 15 or less.

1. Check that walls are continuous through the height of the building and that their shear centre coincides with the line of resultant horizontal loads.
2. Check that walls within any storey height are not slender.
3. Check that the section complies with fire resistance requirements.
4. Check that cover and concrete comply with durability requirements.
5. Calculate axial loads and moments.
6. Design section and reinforcement.

The durability requirements include: (a) An upper limit to the water/cement ratio (b) A lower limit to the cement content (c) A lower limit to the thickness of the cover to the reinforcement (d) Good compaction (e) Adequate curing.

† These walls may have less than 0.4% reinforcement

• These walls to have between 0.4% and 1% reinforcement ** These walls to have more than 1% reinforcement

1. Calculate the axial load on the wall to obtain the most onerous conditions using the partial safety factors for loads.

2. Assume that the beams and slabs transmitting forces into the wall are simply supported.

3. Calculate the horizontal forces in accordance with the provisions of clause 2.6(e).

4. Calculate the in-plane moments for each lift of the wall, assuming the walls act as cantilevers.

5. The moment to be resisted by any one wall should be in the same ratio to the total cantilever moment as the ratio of the wall's effective height.

For mild exposure conditions, the cover to all reinforcement should be:

• 25 mm for the first column
• 20 mm for the second and third columns

The maximum free water/cement ratio for walls in very severe exposure conditions is 0.55.

The minimum cement content required for walls in moderate exposure conditions is 300 kg/m³.

The stresses on the walls from the loads and moments should be calculated using the expression:

extreme fibre stresses, f₁ = N/Lh ± M/hL²/6 N/mm²

where:

• N is the ultimate axial load in N
• M is the ultimate in-plane moment in Nmm
• L is the length of the wall in mm
• h is the thickness of the wall in mm

The ultimate load capacity for walls is given by:

0.35fc Ac + 0.7fy, Asc

where:

• fc is the characteristic concrete cube strength in N/mm²
• Ac is the area of concrete in mm² per mm length of wall
• As is the area of vertical reinforcement in mm² per mm length of wall
• fy is the characteristic strength of reinforcement in N/mm²

The total tension is calculated using the formula: total tension = 0.5 * f * L * h, where f is the extreme fibre stress in tension in N/mm², L is the length of the wall in mm where tension occurs, and h is the height of the wall.

The minimum area of vertical reinforcement in the wall should be 0.4% of the gross cross-sectional area of the concrete on any unit length, and it should be equally divided between the two faces of the wall.

The section should first be designed for the case in clause 4.6.4.1, and then checked for transverse moments, treating each unit length as a column and providing additional reinforcement if necessary.

For openings in shear walls, adequate reinforcement should be provided in the form of diagonal bars positioned at the corners of the openings. This reinforcement should resist a tensile force equal to twice the shear force in the vertical components of the wall, but should not be less than two size 16 bars across each corner of the opening.

The maximum spacing of vertical bars should not exceed:

1. 250mm for steel fy = 250N/mm²
2. 200mm for steel fy = 460N/mm².

The maximum area of vertical reinforcement should not exceed 4% of the gross cross-sectional area of the concrete in a metre length.

Staircase slabs and landings should be designed to support the most unfavourable arrangements of design loads. This is typically satisfied by:

1. Designing to resist moments and shear forces from the maximum design ultimate load on all spans.
2. Considering maximum load on cantilevers exceeding one-third of the span length.
3. Dividing loads equally between intersecting slabs at right angles in open wells.

The effective span for stairs spanning between beams or walls is defined as the distance between the centre-lines of the supporting beams or walls.

The effective span for stairs spanning between landing slabs is defined as the distance between the centre-lines of the supporting landing slabs, or the distance between the edges of the supporting slabs plus 1.8m, whichever is smaller.

When vertical support is not provided at the ends of stair flights, the flights should be designed for the full landing loads. The effective spans must comply with clauses 4.7.4.1 and 4.7.4.2.

The schematic diagram includes the following key components:

• Supporting walls
• Span A
• Span B
• Span C
• Areas common to both spans
• Supporting beam

A pile cap is a foundation type that acts as a pad, strip, combined, or balanced footing, transmitting forces to the soil through a system of piles. It ensures that the load from the structure is distributed evenly across the piles, providing stability and support.

The plan area of foundations should be proportioned based on the following assumptions:

1. All forces are transmitted to the soil without exceeding the allowable bearing pressure.
2. For axially loaded foundations, reactions to design loads are uniformly distributed per unit area or per pile, with eccentricity not exceeding 0.02 times the length in that direction.
3. For eccentrically loaded foundations, reactions vary linearly across the footing or pile system, with zero pressure occurring only at one edge.
4. All parts of a footing in contact with the soil are included in the assessment of contact pressure.
5. It is preferable to maintain foundations at one level throughout.

For unreinforced pad footings with a concrete strength of fcu = 20N/mm², the depth-to-projection ratio (h/a) should be:

Additionally, the ratio h/a must not be less than 1, and the depth h should not be less than 300mm.

The design of axially loaded reinforced pad footings is carried out in three stages:

1. Determine the depth of the footing from the ratios of the overall depth (h) to the projection from the column face (a), as given in relevant tables for different values of unfactored ground pressures (q).
2. Ensure that the effective depth (d) is not less than 300mm.
3. Further design considerations based on structural requirements and load conditions.

The formula is: v = 1000N / (2 (Cx + Cy) d), where v should not exceed ve = 0.8√fcu or 5N/mm².

If v exceeds ve, increase the depth of the footing.

Enter Table 39 with the chosen depth to obtain the corresponding reinforcement percentage.

Determine the initial depth of the footing from Table 39 using the maximum value of unfactored ground pressure.

Check punching shear according to clauses 4.2.3.4 and 4.2.5.2.

Strip footings should be designed as pad footings in the transverse direction and in the longitudinal direction at free ends or return corners, with reinforcement in both directions if required.

• Punching shear should be checked for critical perimeters around closely spaced columns.
• Bending moments should be checked at the point of zero shear between columns, with reinforcement in top and bottom faces.
• For a balanced footing with two pad footings joined by a beam, the beam design follows subsection 4.4.
• Steps in the top or bottom surface may be introduced if accounted for in the design.

• Reinforcement should be in two orthogonal directions with areas not less than:
  • Grade 460: 0.0013bh
  • Grade 250: 0.0025bh
• Reinforcement must extend the full length of the footing.
• If lx > 1.5(cx + 3d), at least two-thirds of the reinforcement parallel to ly should be concentrated in a band width (cx + 3d) centered at the column.
• Spacing between centers of reinforcement should not exceed:
  • Grade 460: 200mm
  • Grade 250: 300mm

The design of a raft must ensure:

1. Equilibrium: Matching column loads with ground bearing pressure.
2. Compatibility: Matching the relative stiffness of the raft and soil.
3. Load Concentration: Allowing for loads concentrated by slabs or beams over supports.
4. Allowable Bearing Pressure: Staying within limits determined by geotechnical strength and settlement considerations.

If a realistic distribution of ground bearing pressure cannot be determined simply, a more complex analysis is required.

The spacing of piles should generally be three times the pile diameter.

The initial depth of the pile cap should be equal to the horizontal distance from the centerline of the column to the centerline of the pile furthest away.

Check the face shear as for reinforced pad footings, using factored loads, and increase the depth if necessary.

Calculate the bending moments and the reinforcement in the pile caps using the factored loads.

For Grade 460, the minimum reinforcement is not less than 0.0013 * bh in each direction. For Grade 250, it is 0.0025 * bh in each direction.

The reinforcement should be continued past the piles and bent up vertically to provide full anchorage past the centerline of each pile.

The types of ties that must be checked include:

1. Peripheral ties
2. Internal ties
3. External column or wall ties
4. Vertical ties

The forces are derived from a 'tie force coefficient' defined as:

• F₁ = (20 + 4*n) kN for n ≤ 10
• F₁ = 60 kN for n > 10, where n is the number of storeys.

Peripheral ties should be located in zones within 1.2m from the edges and should be capable of resisting a tie force of 1.0 F₁, fully anchored at all corners.

Internal ties should be present in two directions approximately at right-angles to each other, capable of resisting a tie force of 1.0 F₁ kN per metre width, provided that the floor spans do not exceed 5m and the total characteristic load does not exceed 7.5 kN/m².

The length of the loadbearing wall between lateral supports should be considered in lieu of the spans.

External columns and loadbearing walls should be tied to the floor structure, with corner columns tied in both directions. The tie force for each column and each metre length of wall is 1.0F, for clear floor-to-ceiling heights not exceeding 2.5m, increasing pro rata for greater heights, up to a maximum of 2.0F,.

The tie force should in no case be assumed to be less than 3% of the total design ultimate load carried by the column or wall.

Vertical ties should be present in each column and loadbearing wall, capable of resisting a tensile force equal to the maximum total design ultimate load received from any one floor or roof.

Laps and splices should be positioned away from zones of high stress and preferably staggered. The lap length for tension bars should be at least equal to the design tension anchorage length necessary to develop the required stress.

If a lap occurs at the top of a section with minimum cover less than twice the size of the lapped reinforcement, the lap length should be multiplied by 1.4. If it occurs at a corner with similar cover conditions, it should also be multiplied by 1.4. If both conditions apply, the lap length should be multiplied by 2.0.

The tension anchorage and lap lengths for reinforcement type 250 at a concrete strength of 30 N/mm² are:

The minimum lap length for bar reinforcement should not be less than 15 times the bar size or 300mm, whichever is greater.

The compression anchorage lengths for reinforcement type 460 across different concrete strengths are:

The note indicates that if the reinforcement acts at a lower stress than its design strength (0.95 fy), the anchorage and lap lengths may be reduced proportionately.

The minimum lap length should be at least 25% greater than the compression anchorage length necessary to develop the required stress in the reinforcement.

Lap lengths for unequal size bars (or wires in fabric) may be based on the smaller bar.

The minimum radii to which reinforcement may be bent can govern aspects of design such as depths of bearings and the choice of bar size for a given thickness of slab.

Mechanical splices may be used in lieu of laps to reduce congestion of reinforcement.

Table 41 provides information on minimum radii, bend and hook sizes, and effective anchorage lengths for bends and hooks for different grades of bars.

Effective anchorage lengths are crucial as they ensure that the reinforcement can develop the required stress, and they are given as multiples of bar size according to standards.

In every flexural member except at end supports, every bar should extend beyond the point at which it is no longer needed for a distance at least equal to the greater of:

1. The effective depth of the member
2. Twelve times the bar size

Additionally, for a bar in the tension zone, it should extend to one of the following distances:

• An anchorage length appropriate to its design strength (0.95fy) from the point where it is no longer required to assist in resisting the bending moment.
• To the point where the design shear capacity of the section is greater than twice the design shear force at that section.
• To the point where other bars continuing past that point provide double the area required to resist the design bending moment at that section.

Staggering the curtailment points of reinforcement is essential because curtailment of substantial areas of reinforcement at a single section can lead to the development of large cracks at that point. This practice helps distribute stresses more evenly and reduces the risk of cracking.

When designing corbels and nibs, the following considerations should be taken into account:

• Design and detail in accordance with the appropriate clauses in the precast concrete section of BS 8110.
• Adequately assess the horizontal forces arising from restrained temperature and moisture movements, as these forces often govern the design.

The key dimensions and symbols in the continuous beams diagram include:

• 0.25le at the top
• 0.15le with an angle symbol <45 degrees below
• Percentages marked as 30%, 100%, 100%, 60%, and 20% along the beam's length
• d marking the depth of the beam
• A smaller vertical line segment marked with d/2
• Text indicating 0.15le and (0.1le for end support)
• le = effective span

The continuous slab diagram includes the following dimensions:

• 0.3le at the top
• 0.15le with an angle symbol <45 degrees below
• Lengths labeled as 40%, 100%, 100%, and 50% along the slab
• d marking the depth of the slab
• A smaller vertical line segment marked with d/2
• A vertical dimension line labeled 0.2le extending from d/2 to the top of the slab
• le = effective span

The 'Full tension anchorage length' in the beam and slab system diagram indicates the required length of reinforcement that must be anchored to ensure structural integrity. Key features include:

• Dimension shown as 0.15le with an angle symbol <45 degrees
• Reinforcement labeled as As/2 at the bottom of the hook portion
• A dotted line indicating reinforcement curtailed as shown in a previous figure
• le = effective span is also noted, emphasizing the relationship between the anchorage length and the effective span of the structure.

A cantilever beam is fixed at one end and free at the other. Key dimensions include 'd', 'd/2', and 'le', with additional labels indicating '0.5le' and '45°'.

0.13% of gross cross-section

M / (0.8d) (0.95fy), where M is the maximum bending moment per metre width anywhere in the slab

0.011 (A'sx + A'sy) kg/m², where A'sx and A'sy are areas of reinforcement selected per metre width in two orthogonal directions

M represents the maximum bending moment per metre width anywhere in the slab for one-way spanning slabs, and the maximum bending moments per metre width in each direction for two-way spanning slabs.

0.24% of gross cross-section

The minimum reinforcement for ribs using high yield steel is 0.25% of the product of the average width of the ribs (bw) and the overall depth of the slab (h).

The minimum reinforcement for structural topping using mild steel is 0.24% of the gross cross-section of the topping.

For one-way spanning slabs, the area of reinforcement is calculated as:

1. M / 0.95fy (d - 0.5hr)
2. For fabric reinforcement: 1.25 x wt/m² of fabric
3. For loose bar reinforcement: 0.009 (sum of bar areas per m width in each direction)

Where M is the maximum bending moment per rib anywhere in the slab.

For two-way spanning slabs on linear supports, the area of reinforcement is calculated as:

1. M / 0.95fy (d - 10 - 0.5hr)

Where M is the maximum bending moment per rib in the two directions.

For coffered slabs on column supports, the bending moment requirements are:

1. Mx / 0.95fy (d - 0.5hr)
2. My / 0.95fy (d - 20 - 0.5hr)

Where Mx and My are the mean maximum bending moments per rib in each direction.

The minimum longitudinal steel reinforcement required for high yield steel is 0.25% of the width of the beam (bw) multiplied by the overall depth of the beam (h).

The minimum reinforcement for links is calculated based on shear stress design:

• If shear stress (v) > 0.6 N/mm²:

  • A'sv / S'v = bw (v - 0.6) / 0.95fy

• If shear stress (v) ≤ 0.6 N/mm²:

  • Choose A'sv and S'v to satisfy minimum steel requirements.

The required longitudinal steel at midspan for T- and L-beams is calculated using the formula:

M / 0.95fy (d - 0.5hf)

where M is the design ultimate bending moment, fy is the yield strength, d is the effective depth, and hf is the flange thickness.

The weight specification for longitudinal steel reinforcement in beams is 0.011A's per square meter, where A's is the area (in mm²) of the main reinforcement selected at midspan or supports, whichever is greater.

The minimum reinforcement for mild steel is 0.50% of the width of the beam (bw) multiplied by the overall depth of the beam (h).

The minimum longitudinal steel reinforcement required for columns is 1% of the necessary concrete area.

Links must satisfy the following requirements:

1. Size: At least one-quarter of the biggest longitudinal bar.
2. Spacing: 12 times the size of the smallest longitudinal bar, but not more than 300mm.
3. Every corner and each alternate longitudinal bar should be restrained by a link in each direction.

The minimum vertical reinforcement required for walls is 0.4% of the cross-sectional area.

The minimum horizontal reinforcement required for walls is 0.2% of the cross-sectional area.

The weight of reinforcement in kg/m² of wall elevation is calculated using the formula: 0.011 (A + Ash), where Asv and Ash are areas of reinforcement in mm² selected per metre width and height.

The formula for calculating the reinforcement ratio (ρ) is: ρ = Asc / (b * h) where Asc is the area of the tensile reinforcement, b is the width of the section, and h is the overall depth of the section.

The ratio d/h, where d is the effective depth and h is the overall depth, is critical in determining the efficiency of the reinforcement. A ratio of d/h = 0.95 indicates a high effective depth relative to the overall depth, which can enhance the structural performance.

The parameter ρfy/fcu represents the ratio of the reinforcement ratio multiplied by the yield strength of the reinforcement (fy) to the characteristic compressive strength of concrete (fcu). A value of ρfy/fcu = 1.4 indicates a specific balance between the reinforcement and concrete strengths, which is essential for ensuring adequate structural performance under load.

The graph illustrates the relationship between the normalized axial load (N/bhfcu) and the normalized moment (M/bh²fcu) for different values of the parameter ρfy/fcu. It shows how these two factors interact under varying conditions of reinforcement, which is crucial for understanding the behavior of reinforced concrete structures under combined loading conditions.

The chart shows the relationship between N/bhfcu on the y-axis and M/bh^2fcu on the x-axis, with multiple curves representing different values of ρfy/fcu. The curves initially increase and then decrease, forming humps at various points along the x-axis, indicating how these parameters interact under different conditions.

The values labeled on the curves (0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4) represent different parameters of ρfy/fcu, which affect the relationship between N/bhfcu and M/bh^2fcu. These values help in understanding how varying the reinforcement ratio influences structural behavior.

These terms refer to the classification of reinforcing bars in the cross-section. Bars included in calculating Asc are those that contribute to the area of steel reinforcement, while bars not included do not contribute to this calculation, affecting the overall structural capacity and behavior as illustrated in the chart.

The relationship between d and h is given as d/h = 0.90, indicating that the depth of the effective reinforcement (d) is 90% of the total height (h) of the cross-section, which is a critical factor in structural design calculations.

The graph illustrates the relationship between the normalized axial load (N/bhfcu) and the bending moment (M/bh^2fcu) for a reinforced concrete section, showing a family of curves for different values of pfy/fcu.

The parameter ρ is defined as Asc/bh, representing the ratio of the area of steel reinforcement (Asc) to the product of the width (b) and height (h) of the concrete section, which is crucial for understanding the reinforcement design.

The ratio d/h = 0.85 indicates the effective depth (d) relative to the overall height (h) of the column, which is important for determining the moment capacity and overall structural behavior of the column.

'N/bhfcu' represents the normalized axial load on reinforced concrete columns, where 'N' is the axial load, 'b' is the width, 'h' is the height, and 'fcu' is the characteristic compressive strength of concrete.

The graph illustrates that as the axial load capacity (N/h²fcu) increases, the bending moment capacity (M/h³fcu) also varies depending on the reinforcement ratio (pfy/fcu). Different curves represent different reinforcement ratios, indicating that higher reinforcement ratios can lead to increased bending moment capacities for a given axial load capacity.

The reinforcement ratio (pfy/fcu) significantly influences the relationship between axial load and bending moment capacities. Higher reinforcement ratios typically result in:

1. Increased bending moment capacity for a given axial load capacity.
2. Enhanced structural performance and stability of the column under combined loading conditions.

This is reflected in the distinct curves on the graph, where each curve corresponds to a specific reinforcement ratio.

The graph shows the relationship between the axial load parameter (N/h²*fcu) on the vertical axis and the moment parameter (M/h³*fcu) on the horizontal axis, with curves representing different reinforcement strengths based on the ratio pfy/fcu.

The curves in the graph are labeled according to different values of pfy/fcu, indicating how the yield strength of the reinforcement relative to the concrete compressive strength influences the relationship between axial load and moment parameters.

The ratio hs/h = 0.6 indicates the geometric relationship in the cross-section of the column, which is important for understanding the distribution of reinforcement and its effectiveness in resisting loads.

The variable p represents the ratio of the total area of reinforcement to the cross-sectional area of the column, calculated as p = 4Asc/πh², which is crucial for determining the adequacy of reinforcement in structural design.

The key updates in the second edition include:

1. Amendments to BS 8110, republished in 1997 and further amended in 2001.
2. The publication of BS 8002 for the design of earth retaining structures.
3. The publication of BS 8666, which superseded BS 4466.
4. Modifications to some span/depth values for initial design based on feedback from practising engineers.