Concrete Slab/Wall Design |
  
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Concrete Slab/Wall Design |
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General
The concrete slab/wall module designs concrete slabs or walls against enveloped positive and negative Wood-Armer bending moments in slab local x and y directions. Axial force action is ignored. The program produces contours of required areas of steel which can be averaged with some commonsense to finish the design.
Wood-Armer Moments
Wood-Armer Formula [Ref 18, pp198] is the most popular approach to convert Mx, My and Mxy to orthogonal plate design moments Mux and Muy
The procedure to obtain Mux and Muy for designing plate bottom reinforcement is as follows:
•Mux = Mxx + |Mxy|
Muy = Myy + |Mxy|
•If Mux < 0 and Muy < 0
Mux = 0
Muy = 0
If Mux < 0 and Muy > 0
Mux = 0
Muy = Myy + |Mxy * Mxy / Mxx|
If Mux > 0 and Muy < 0
Muy = 0
Mux = Mxx + |Mxy * Mxy / Myy|
•Mux >= 0
Muy >= 0
The procedure to obtain Mux and Muy for designing plate top reinforcement is as follows:
•Mux = Mxx - |Mxy|
Muy = Myy - |Mxy|
•If Mux > 0 and Muy > 0
Mux = 0
Muy = 0
If Mux > 0 and Muy < 0
Mux = 0
Muy = Myy - |Mxy * Mxy / Mxx|
If Mux < 0 and Muy > 0
Muy = 0
Mux = Mxx - |Mxy * Mxy / Myy|
•Mux <= 0
Muy <= 0
Wood-Armer Formula is a lower bound solution method which satisfies the following conditions for a given external load:
•The equilibrium conditions are satisfied at all points in the plate.
•The yield strength of the plate elements is not exceeded anywhere in the plate.
•The boundary conditions are complied with.
A lower bound solution is conservative in nature.
Stress Singularity
The stresses and bending moments at the point of a concentrated load on the slab are theoretically infinite. This theoretically means that if we used all the steel in the world, we still did not have enough steel to resist the stress at that point. This is of course ridiculous. The reason is of course because we prescribe an impossible loading (“concentrated load”). If we distribute the load over a small area (circle), the stresses become finite.
In finite element analysis, the program will never give you a stress of infinite magnitude. Still, at a point of concentrated force such as a column acting on a flat plate, stresses may have rather significant spikes. According to Ugural [Ref 15, pp116], the actual stress caused by a load on a very small area of radius rc can be obtained by replacing the actual rc with an equivalent radius re.
(rc > 0.5t)
(rc <= 0.5t)
where t is the plate thickness.
By applying this method, we can use stresses at half of the slab thickness instead of those at the concentrated loading point. By excluding the finite elements (usually finely meshed) near the concentrated loading points, we can provide practical and reasonable design results.
The plate top and bottom flexural reinforcement in local x and y direction is computed at each nodal point as well as the center. No minimum reinforcement is considered. The program only designs each plate with tension-controlled condition. The procedure is similar to that of concrete beams except no double reinforcement is considered.
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