Plastic section modulus of a plate

Question

Good Morning I am modeling hard rock tunnel and using plates as my shotcrete support. My plates are modeled as Elastoplastic and hence I need to input strength parameter W11 which I am confused regarding equation to be used. Manual indicate plastic section modulus to be bd2/6 in beam section of the manual, I however recall that plastic section modulus shall be bd2/4. My plates are mostly under compression with low bending moment induced.

Vasileios Basas · Answer

Hi Michal, 
 You are correct. There is an error in our Reference Manual, so the section modulus we use internally is the elastic section modulus and NOT the plastic section modulus . Given that the plate has (always) a rectangular cross-section, the elastic section modulus (W) is calculated based on the following formula: 
 W = I / y 
 where I = moment of inertia and y = distance from the centroid to the top or bottom edge of the rectangle. For a prismatic beam (plate): 
 I = (1/12)b x h 3 and y = h/2 => W = ( b x h 2 ) / 6 
 You can refer to Chapter 6.4.2 (Mechanical Properties) of the Reference Manual and Chapter 18.6 (3D Plates) of the Material Models Manual for more information

Dennis Waterman · Answer

Dear Michal, 
 The part of the manual you're referring to is not about scaling the results of the calculation, but scaling the full plastic bending moment input. Because PLAXIS assumes that a plate element has a simple rectangular cross section (whereas in reality it may be a sheet pile wall or a T-shape element wall etc) with a single value of the yield stress one cannot have both the Np and the Mp correct. So if the yield stress is chosen such that for the rectangular cross section Np is correct, then Mp is overestimated. This means that one should check the output results for bending moments to see if they don't overestimate the real Mp since PLAXIS calculated with an overestimated Mp. But if the bending moments are smaller than the real Mp, there is no need to factor them down as they will be correct. Hence, it's not the bending moments that should be factored down, it's the bending strength that should be factored down. 
 With kind regards, 
 Dennis Waterman