D. BS8110 Beam Design Principles
The BS8110 Beam Design Brief is for single or multi span, prismatic, rectangular solid or tee shaped members. The member sections must be defined as PRISMATIC sections in the STAAD.Pro data file.
Refer to D. Suitable Member Properties for more details.
Beams are designed for bending, shear and deflection. They may also be checked for Torsion. Sections are taken at equal increments along each span of the beam and at the positions of maxima of hogging and sagging moments and maximum positive and negative shear.
Design for Bending
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. Compression reinforcement is provided where required.
The design of a beam is based on an envelope of design forces and 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, those that can use the same cage
- Same size
- Same covers
For each sub-beam, the sections that have 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 programs limits design to 8 bars in any one layer and uses a maximum of 2 layers in each face.
The program then goes along the beam and checks each section to see 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 torsional 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, vc . 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.
Minimum shear links required,V, for shear forces between these values
Design for Torsion
The method for designing a beam with a rectangular section to resist torsion is as follows. It consists of calculations to determine an additional area of longitudinal and link reinforcement required to resist the torsional shear forces.
- Determine As and Asv to resist the bending moments and shear forces by the usual procedures.
Calculate the torsional shear stress ( for rectangular) clause 184.108.40.206where
- torsional moment due to the ultimate loads
- the smaller dimension of the beam section
- the larger dimension of the beam section
If vt > vtmin in table 2.3, then torsional reinforcement is required. Refer table 2.4 for the reinforcement requirements with a combination of torsion and shear stress v.
but not more than 0.4 N/mm2
but not more than 5 N/mm2
Table 1. Table 2.4 Reinforcement for shear and torsion vt ≤ vtmin vt > vtmin
v ≤ vc + 0.4
Minimum shear reinforcement; no torsion reinforcement
Designed torsion reinforcement but nor less than the minimum shear reinforcement
v > vc + 0.4
Designed shear reinforcement; no torsion reinforcement
Designed shear and torsion reinforcement
Calculate the additional shear reinforcement required from torsion (as per clause 2.4.7 )
Sv < 200 mm or x1
Where x1 is smaller center-to-center dimension of a link.
y1 is larger center-to-center dimension of a link.
- Calculate the additional area of longitudinal steel. (as per clause 2.4.7 )
For beams formed from Tee and L shaped profiles, each cross section is divided into rectangles so that the stiffness is maximized as defined in clause 220.127.116.11. The rectangle with the largest h3 min . hmax is then checked to ensure that the torsional shear stress does not exceed the limits and the maximum link spacing is based on this rectangle.