# D. AIJ Beam Design Principles

The AIJ 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 flexure, and shear only. 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. The user can specify the number of segments to be considered between 4 and 25 for each member.

## 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. 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 8 bars in any one layer and uses a maximum of 2 layers.

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 procedure

Fy – allowable unit stress for reinforcement bars is calculated based on Table 5 and considers both temporary and permanent loading

- Calculate balanced Pt based on Art. 14 , equation 9.
- Calculate Neutral axis ratio based on Art. 14, equation 8.
- Calculate C based on Art. 14, equation 7.

Allowable bending moment = Cbd^{2}

Gamma is considered to be 0.4 to begin with for light weight concrete.

The area of reinforcement, At, is calculated using Art. 14.3, equation 14 when the allowable bending moment is greater than the design moment.

An iterative method is used to calculate area of reinforcement required when design moment is greater than allowable moment.

- First program tries to increment compression reinforcement by incrementing gamma.
- If gamma reaches 1.0, then program increments tension reinforcement and recalculates C.
- The design fails if the tension reinforcement exceeds maximum reinforcement.

## 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, 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.

### Minimum shear links required,V, for shear forces between these values

Shear capacity is calculated in accordance with Art. 16.2.1, equation 22

fs is calculated in accordance with table 4.

To calculate 'pw', spacing is first assumed to be 45 cm. and the program runs through a iterative method and reduces the spacing to establish the actual required spacing.

The design checks for minimum and maximum spacing as per Art.16.4.ii