D. IS456 Beam Design Principles
The IS456 Beam Design Brief is for single or multi span prismatic, rectangular members. The member sections must be setup in the Section Property Calculator and assigned from the User section database.
Beams are designed for flexure and shear. Each member is divided into equally spaced sections and the locations of maximum positive and negative moments along each element that makes up the member. You may specify the number of segments to be considered between 4 and 25 for each member.
Both Ultimate limit state and Serviceability Limit states will be considered. Serviceability Limit states will be taken into account by satisfying the span/effective depth ratios specified in Cl. 23.2.1 of the code.
Partial Safety factors
The partial safety factors for materials used for member design are as follows:
- Γm for concrete = 1.5
- Γm for steel =1.15
Design for Flexure
The main (longitudinal) reinforcement is calculated for both sagging and hogging moments on the basis of the section profile and parameters defined in the Design Brief. Lateral bending are considered if this option is selected. Compression reinforcement is provided where required.
The design for flexure is performed as per Cl. 38 of the code.
The design of a beam is based on an envelope of design forces. Thus, at each of the defined sections the program determines the required area of steel for both the maximum hogging moment and maximum sagging moment at that section.
The beam is then divided into sub-beams. The sub-beams which can use the same reinforcing cage are those with:
- Same size
- Same covers
For each sub-beam, the sections with the largest sagging and hogging moments are identified and the most efficient reinforcement is calculated for the range of bars specified in the Design Brief. The program is limited to eight bars in any one layer and uses a maximum of two layers.
The program then checks each section along the beam to determine how many bars from the critical sections can be removed. The bars are only removed at the section if they are not required for compression reinforcement or would result in failure in a crack check.
Design for Shear
The shear reinforcement is designed to resist the major axis shear force envelope, Fz, acting through the beam. The minor axis shear and tensional forces are not considered.
The number of shear legs and the shear link size is specified in the Design Brief. Therefore, the required spacing for minimum links can be defined. The program then checks each section to determine the shear stress v and concrete shear capacity v_{c}. From this, the section is classified as either minimum link or a high shear section. Adjacent sections of the same type are grouped into zones. For non minimum link zones, the shear links are designed for the maximum shear force within that zone.
If necessary, additional legs may be added to the shear links in order to restrain tension or compression reinforcement.
The design for shear reinforcement is performed as per Cl.40 of the code. The nominal shear stress in beams is evaluated as:
τv = V / bd |
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The design shear strength of concrete is taken as specified in Cl. 40.2 of the code. For members in axial compression, the design shear strength is multiplied by the following factor:
δ=1+ (3 P_{u})/(A_{g} x f_{ck}) |
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Design for shear reinforcement is based on Cl.40.3 to 40.5 of the code. Note that the design brief includes the option of selecting whether to consider enhanced shear effects near the supports of the beam. If the option to consider enhanced shear is selected, the program also considers Cl.22.6.2 when working out the shear links.
Design for Torsion
The design of beams considers the combined effect of shear and torsion per Cl. B-6.3 of IS 456-2000.
The design for torsion is based on Cl. 41.3 of IS 456. This method involves working out an equivalent bending moment and equivalent shear based on the torsional moment at a particular section. The equivalent shear force for torsion design is evaluated as:
V_{e} = V_{u} + 1.6 T_{u}/b, |
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The longitudinal reinforcement required at a particular section subject to torsion is evaluated based on an equivalent bending moment evaluated as:
M_{e} = M_{u} + M_{t} |
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The distribution of torsion reinforcement will then be done as per Cl. 26.5.1.7 of IS456.
The number of shear legs and the shear link size is specified in the Design Brief. Therefore, the required spacing for minimum links can be defined. The program then checks each section to determine the shear stress v and concrete shear capacity, v_{c}. From this, the section is classified as either minimum link or a high shear section. Adjacent sections of the same type are grouped into zones. For non minimum link zones, the shear links are designed for the maximum shear force within that zone.
If necessary, additional legs may be added to the shear links in order to restrain tension or compression reinforcement.