# 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

1. Same size
2. 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.

## 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.

1. Determine As and Asv to resist the bending moments and shear forces by the usual procedures.
2. Calculate the torsional shear stress ( for rectangular) clause 2.4.4.1

$v t = 2 T h min ⁡ 2 ( h m a x − h min ⁡ / 3 )$
where
 T = torsional moment due to the ultimate loads hmin = the smaller dimension of the beam section hmax = the larger dimension of the beam section
3. 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

4. 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.

5. 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 2.4.4.2.  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.

## Anchorage and Bond Lengths

Anchorage and bond lengths are calculated in accordance with the requirements of clause 3.12.8.  They can be displayed graphically on the Main Reinforcement diagram and are used for the schedule table and export to Multi-RC.