The UMomPF function returns ultimate bending and axial load capacity to the Eurocode 2 and BS 5400 design codes. It has now been updated to also return shear capacity, and modified bending capacity, allowing for the additional tensile force in the longitudinal steel due to the shear force. Note that in the current version there is no provision for design for torsion.

The main data input array is the same as for the UMom function:

Shear reinforcement and related data input is different to UMom:

The last two input values are only required for Eurocode 2:

The shear capacity in Eurocode 2 is calculated with a strut and tie model. The angle of the compression strut to the horizontal is specified by the Cotangent of the angle, which must be in the range 1.0 to 2.5.

The additional longitudinal tension is limited to the force that would increase the applied bending moment at the section to more than the maximum moment along the beam.

If the Cot(strut angle) input is not entered (or is outside the range 1.0 to 2.5) the function adjusts the angle so that the maximum shear controlled by concrete compression is equal to the shear capacity of the shear reinforcement:

In this example the shear capacity (712 kN) is well over the applied shear, but the adjusted moment capacity (492 kNm) is less than the applied moment.

Entering a Cot Theta value of 1.2 reduces the shear capacity and also reduces the additional longitudinal force:

The reduced shear capacity of 508 kN is greater than the applied shear (500 kN), but the adjusted moment capacity (547 kNm) is still just under the bending moment at the section.

Entering a moment of 650 kNm as the maximum moment along the beam reduces the additional longitudinal force to 207 kN, and the adjusted bending capacity increases to 589 kNm:

The shear capacity calculation in BS 5400 is simpler, and the Cot Theta and maximum moment values input have no effect on the results:

In this case the shear capacity is greater than the final value found using Eurocode 2, but the bending capacity is significantly lower, and after adjustment for shear it is below the required value.