Layered shell, comparison with ETABS

Results.

Problem. Two plates with layered sections, a steel-concrete composite plate and a five-layer CLT floor, are solved separately with MindFEM and with ETABS. The composite plate has an unsymmetric stack, so membrane action and bending affect each other; in the CLT floor the cross layers at mid-depth have a low transverse shear stiffness. Deflections, bending moments, membrane forces and the shear forces beside the supports are compared.

Reference document. The reference is the same plates modelled in ETABS 20.1.0 with a layered shell section. The CLT lamellas are given in ETABS as an orthotropic material, with the layers at 0° and 90°.

Numerical model. The composite plate is 6 × 6 m, 200 mm of C30/37 concrete on a 12 mm S355 steel plate; the CLT floor is 5 × 4 m, five layers and 200 mm thick, with the outer lamellas along x (C24, E0 = 11 GPa, E90 = 0.37 GPa, G = 0.69 GPa, rolling shear modulus 0.069 GPa). Both plates are simply supported on all four edges, with the vertical displacement and the rotation along the edge held, and the mesh is made of 0.25 × 0.25 m quadrilateral elements.

Steel-concrete composite plate#

Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects

Note. G is the self weight with 2 kPa finishes, Q a 5 kPa live load. The reference surface is at the middle of the total thickness. The stack is unsymmetric, so membrane forces arise in the plate under vertical load too; the Nxx and Nyy rows show that interaction. The nodes read are the plate centre, the quarter point (1.5; 1.5) and the edge midpoints 0.25 m inside the supports. The ETABS moment sign convention is the opposite of MindFEM's, and the table uses MindFEM's sign. The moment across the support next to it rises quickly from zero at the support, differs by 4 per cent between the two programs and is left out.

CLT floor, with the transverse shear assumption of ETABS#

Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects

Note. G is the self weight with 1.5 kPa finishes, Q a 2 kPa live load. The layered shell of ETABS takes the transverse shear stiffness as the sum of the shear modulus times the thickness of the layers. In this example MindFEM is given the same stiffness: the transverse shear moduli of the layers are entered 1.2 times larger with the uniform shear model (5/6 × 1.2 = 1). The nodes read are the plate centre, the quarter point (1.25; 1) and the edge midpoints 0.25 m inside the supports. The shear force beside the x = 0 support differs by 6.8 per cent between the two programs; the difference is the same in the next example and does not come from the shear assumption.

CLT floor, with layered transverse shear#

Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects

Note. This table is not a verification. The default layered model of MindFEM derives the transverse shear stiffness from the shear flow through the section and reproduces the 2D plane-stress solution for a five-layer CLT (CLT strip page). The cross layers at mid-depth have a low rolling shear modulus, and this model weighs their share by where they sit in the section. The assumption of ETABS counts these layers at their full thickness and shows the CLT floor stiffer. The difference is 8 to 9 per cent in the deflections, while the moments stay within 3 per cent.

Model files#

The ETABS models that produced the results in the tables can be downloaded. They open in ETABS 20 and later with File > Import > ETABS .e2k File.

• Steel-concrete composite plate (.e2k)
• CLT floor (.e2k)