Section 8.1 Strength of Beams in Bending

Reinforcement areas are not deducted from the concrete area.

Strain compatibility design is used. See General Design Approach for a description of RAM Concept ’s strain compatibility design.

See Concrete Stress-Strain Curves and for tendon, concrete and mild steel reinforcement stress strain curves

Capacity reduction factors ɸ are taken from Table 2.2.2(b), (c), and (d).

Flexural capacity is limited to ɸM_uo as required by clause 8.1.5.

During the flexural/axial design in pass 1, an ε_x design is performed in preparation for shear calculations in pass 2. In slabs, the design is performed to limit ε_x to the maximum value that would prevent the need for transverse reinforcement. In beams, ε_x is designed to the maximum value that would satisfy strength using only minimum transverse reinforcement. ε_x is never designed less than 0.001.Equation 8.2.7.1(1) is implemented, with the vertical component of prestress, P_v, taken as zero. When no transverse reinforcement is present, V_us is taken as zero.

To satisfy the requirements of 8.2.8, RAM Concept calculates a shear/torsion tension force calculated per equation 8.2.7.1(1) and adds it to the cross-section demand forces. Because 8.2.1.1(1) is only meant to account for a single face, forces are tracked separately for the top and bottom faces of the section. The shear/torsion tension force will effectively increase the tension demand on the tension face as required by equation 8.2.8.2(1) and reduce the compression demand on the compression face per 8.2.8.3(1). In compression fan regions near supports where the diagonal shear strut angle is steeper, the shear tension diminishes on one face to zero at the face of support, based upon the orientation of the diagonal shear strut. A compression fan region factor is applied near supports to account for this effect.

The designs including shear/torsion tension are enveloped with the strength designs without shear/torsion tension, so the shear/torsion tension forces can only increase the reinforcement and will never reduce it. Equations 8.2.8.2(2) and 8.2.8.3(2) are not directly applied, but RAM Concept ’s approach ensures cross section equilibrium with the additional shear/torsion tension forces as intended by this clause.

User E_s values are used

For sections with multiple values of f’_c, the f’_c of each concrete block is used appropriately.

RAM Concept ’s design may exceed the maximum amount of allowed reinforcement, and therefore may create an over-reinforced section. See Ductility for applying ductility requirements.

If the section or strip is declared as not being post-tensioned, then post-tensioning Tendon forces are ignored.

Axial forces (loads) on the section are either considered or ignored based on the settings in the design section or design strip segment under consideration. If axial forces are chosen to be included, the cross section is designed to provide the required moment simultaneously with the given axial force.

Note: The shear/torsion tension provisions for this standard are handled as a modification to the axial design forces. Therefore, ignoring axial forces in strength design would also ignore the shear/torsion requirements per the standard. Therefore, it is always recommended to include axial forces with strength design.

At "T", "L" and "Z" beams, the beam stem and flanges may have significant tension and compression forces (at different elevations) that are required for moment equilibrium. If a cross section crosses the entire beam, these forces will largely cancel (while increasing the bending moment). However, if a cross section extends only part way across a flanged beam, then the section may have significant axial forces that are required for moment equilibrium; designing for the axial loads (by selecting the appropriate design section or design strip segment properties) is necessary to ensure a safe design.

For cross sections with very small moments, the amount of reinforcement calculated by RAM Concept may exceed the amount necessary. This is because RAM Concept will not allow cross sections to have strains greater than 20%, which would be necessary to create a smaller compression zone. The reinforcement RAM Concept selects is that necessary for axial force equilibrium in the cross section.

The diversion of post-tensioning forces into supports (and other regions of the structure) will cause a hyperstatic (secondary) tension in many cross sections, as is appropriate.

RAM Concept does not consider section 17.3.5, which states that unbonded tendons should only be used on grade; the engineer needs to take this into account before starting the design.

Section 8.3 (General Details for Beams) is partially implemented.