Concrete design moments:(Wood & Armer equations)

The STRAP output tables display the elastic bending and torsional moments at the centre of each element.(Mx, My and Mxy). For reinforced concrete plates, these moments must be translated into equivalent designmoments Mx* and My* which take into account not only the bending moments Mx and My but also the torsionalmoment Mxy. These design moments are then used to calculate the required reinforcement steel.

The calculation of the design moments Mx* and My* is based on the Wood & Armer equations.The postprocessor first calculates the element moments Mx, My and Mxy relative to any orthogonal coordinatesystem chosen (the "result coordinate system"). The design moment calculation assumes that thereinforcement X* axis is parallel to the X axis of the result coordinate system and that the Y* reinforcementaxis is skewed at an angle alpha (usually 90).

A similar calculation must be carried out to derive the design forces Fx* and Fy* from the STRAP results Fx, Fyand Fxy.

Refer also to Element coordinate systems for a more detailed explanation on the result and reinforcementcoordinate systems.

The sign convention for the design moment equations is shown in the following Figure:

The equations are:Moments:

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In-plane forces:

Combined forces:From examination of the equations above, it is obvious that for the general case

Mx |Mxy| and Fx |Fxy|where the worst case is used for each calculation.

When reinforcement is calculated for combined forces, four different combinations of moment and in-planeforces must be checked to determine the worst condition, i.e.

Mx |Mxy| combined with Fx |Fxy|For example, bottom X reinforcement:

Mx + |Mxy| will always be the governing case

For a small negative moment and large tension force, tension reinforcement will be required. Mx - |Mxy| willreduce the design negative moment and hence minimize the bottom compression stress.. Therefore, Mx -|Mxy| (min. compression) combined with Fx + |Fxy| (max. tension) will be the worst case condition formaximum bottom tension.

x Moment only:

x Moment and in-plane force:

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