Section Cut, girder deck

Results.

Problem. A Section Cut cuts shell and frame elements together and can sum only the elements chosen. In a concrete deck on steel I-girders the section forces of the whole deck, of the girders alone and of the slab alone are compared.

Reference document. The whole deck is checked against statics. The girders and the slab are read about the same point, so together they equal the whole deck.

$K$ stands for the girders and $D$ for the slab. No axial load acts on the deck, so the tension in the girders equals the compression in the slab and the two carry the moment as a couple.

Numerical model. The deck spans 30 m, is simply supported and is 10 m wide. The 0.25 m concrete slab is built from shell elements and the four 1500 mm steel I-girders from frame elements, and every girder node is tied to the slab node above it by a Body Constraint.

Concrete deck on steel I-girders, 30 m#

Closed form. Static equilibrium

Note. The girders are 2.5 m apart and their centroids lie 0.875 m below the mid-surface of the slab. The bearings are at the girder ends. Q is a 10 kPa load on a 2.5 m wide strip, 1.25 m from the deck axis. K1 and K2 cut the whole deck, K1-K and K2-K the girders only, K1-D and K2-D the slab only. In all of them the moment is taken about the point on the deck axis at the mid-surface of the slab.

Comparison with composite section theory#

Compared model. Composite section theory (transformed section, full slab width effective)

Note. The theory takes the full width of the slab as effective and the section as staying plane. In the model the couple is smaller than the theory. At midspan the difference is 0.17% under G and 0.54% under Q, which acts on one side of the deck, and at x = 7.5 m, where the shear is large, it rises to 2.4% and 2.9%.

Comparison with SAP2000#

Independent calculation. SAP2000 27.1.0, the same model, Section Cut by SAP2000's own group definition

Note. The SAP2000 model is built with the same nodes and elements, the shells are Shell-Thick and SAP2000 does not mesh them further. The Section Cut uses SAP2000's own definition, a group of the summed elements and the section nodes, and the moment is taken about the same point. The Body Constraint between the girders and the slab is SAP2000's own Body constraint. The whole deck and the couple agree in both programs. Under Q the lateral moment M2, the lateral shear V3 and the torsion of the girders are not in the table. How this lateral action is shared between the slab and the girders depends on the rotational stiffness of the shells in their own plane. With that stiffness reduced tenfold in MindFEM, the girders' M2 at x = 7.5 m rises from 979 to 1158 kNm, against 1065 kNm in SAP2000. The torsion of the girders is 208 kNm in MindFEM and 241 kNm in SAP2000. Over the whole deck these components sum to zero in both programs.

Model files#

The model of the SAP2000 comparison can be downloaded. It opens in SAP2000 27 and later with File > Import > SAP2000 .s2k Text File and carries the Section Cut definitions.

• Concrete deck on steel I-girders (.s2k)