A tie beam is subjected to the action of a tensile force and a uniform lateral load. The tensile force is 21,970 lb and the uniform lateral load is 1.79258 lb/in. The beam is steel and has a square section of 2.5 in by 2.5 in.

Determine the maximum deflection, maximum bending moment and the slope at the lefthand support. In this sample, the effect of geometric stiffening is included by using nonlinear static analysis and compare the results to those in problem 10 where the geometric nonlinearity is ignored.

The model has 9 joints and 8 beam elements. The tensile force is specified as an external force acting at joint 9. The uniform load is specified as an external beam loading.

Modulus of Elasticity = 30,000,000 lb/in2

Span = 200 inches

A = 6.25 in2

Izz = 3.2552 in4

Uniform Load = 1.79253 lb/in

Tensile Force S = 21,970 lb

Nonlinear static analysis is performed using one (1) load step and maximum of 20 iterations.

The nonlinear static analysis includes the geometric stiffening effect of the beam. For comparison of results to the linear static analysis, refer to the previous problem.

Tested Features

App

Object Link : https://openbrim.org/objid06or8s4fbjud7jfsw5jyiwh.project

Library

Object Link : https://openbrim.org/objidjkb7h8u193a9nmca4gu3rt.libobj

Sources

Timoshenko, S., "Strength of Materials, Part II", 3rd Edition, D. Van Nostrand Co., Inc., New York, p. 42.
LARSA 4D

Result Comparison

Timoshenko

LARSA

Openbrim

Percent Difference

LARSA vs. Timoshenko

Percent Difference

Openbrim vs. Timoshenko

Vertical disp at node 5 (in)

-0.200

-0.1995

-0.1996

0.25%

0.2%

Rotation at jt 1 (rad)

-0.0032352

-0.0032

-0.0032

1.1%

1.1%

Moment at i-end of beam 5 (in-Ib)

-4579.91

-4580.0151

4580.4428

0%

0%