Overview

Test Case

This test case models a rectangular frame subjected to a uniform distributed load of 500 lbf/in across the span BC, illustrated in Figure 194. The columns AB and CD are identical with a length of 400 in and a moment of inertia . The horizontal span has a length of 800 in and a moment of inertia five times the moment of inertia of the columns (). All members of the frame have an I-Beam cross-section with the columns following W36x300 dimensions. The ends A and D of the columns are clamped. The objective is to validate the rotation of the rigid connection B and maximum bending moment of the frame.

This problem is also presented in test case VM217 in the Mechanical APDL Verification Manual.

Figure 194: Problem Sketch

The following table lists the main parameters of the test case, which uses the following system of units: length in in, time in s, mass in lbf-s²/in, force in lbf, and pressure in psi.

Analysis Assumptions and Modeling Notes

As shown in Figure 194, the dimensions of a W36x300 I-Beam cross-section used in the columns are = 16.655 in, = 36.74 in, = 0.945 in, and = 1.68 in. This cross-section has a moment of inertia of 2.01389 ⋅ 10⁴ in⁴. For the horizontal span, the I-Beam cross-section dimensions are scaled by a factor of 1.49535 for its moment of inertia to be five times the moment of inertia of the columns.

For a portal frame subjected to a uniform distributed load across its span with and , the rotation of the rigid connection B can be calculated as:

(46)

where

is the column height

and is the Young’s modulus

The rotation of the rigid connection is 1.96168 ⋅ 10^-3 for the current test case. The maximum bending moment of the structure occurs in the middle of its span and can be calculated as:

(47)

For the current test case, the maximum bending moment of the bar is 2.81481 ⋅ 10⁷ lbf-in.

Two parts are defined to represent the horizontal span and the columns of the portal frame, being meshed with 1D beam elements. These elements use Belytschko-Schwer full cross-section integration (ELFORM=4) with an arbitrary cross-section type (QR/IRID=-1, CST=2). The I-Shape cross-section integration rule is defined using *INTEGRATION_BEAM (ICST=1, K=2) with the specific dimensions of each part. Both parts use a linear elastic material card (*MAT_ELASTIC) with properties listed in the table above. The keyword *BOUNDARY_SPC_NODE is used to define the clamped condition of both end nodes, while *BOUNDARY_SPC_NODE_SET is used to constrain the motion of all nodes in YZ plane. The distributed load is prescribed to all beams of the horizontal spam using *LOAD_BEAM_SET. The keywords *CONTROL_IMPLICIT_DYNAMICS (IMASS=0) and *CONTROL_IMPLICIT_GENERAL (IMFLAG=1) are used to activate the implicit static structural analysis.

Figure 195: Model setup in LS-DYNA of the 2D structural analysis of portal frame under symmetric loading

Results Comparison

The visualization of the final configuration of the portal frame subjected to the distributed load can be performed by reading the d3plot file. The maximum bending moment (S-direction beam moment) is located in the middle of the horizontal span, as predicted in theory. To quantify the error between the theoretical and LS-DYNA results, the rotation of the rigid connection and the maximum bending moment of the frame are calculated with their relative errors and shown in the following table. This comparison verifies the agreement between the rotations and bending moments.