Example Description

This model tension stiffening calculation using P-Delta analysis is verified in this example using a tie rod (beam) with a large axial force.
In this example a simply supported, 3-inch-square, steel beam has a large axial force and a small transverse uniform load. The deflection in the direction of the transverse load (global Z direction) is reduced because of the stiffening effect of the tension force. The values of the midpoint deflection and bending moment with and without tension stiffening are calculated and compared with independent results derived using formulas presented in Timoshenko 1956.
Two different methods are used to apply the tension stiffening. In one method, a P-Delta force equal to the specified tension is assigned directly to the beam. The beam is then analyzed in a linear static load case with the transverse loading applied. In the second method, the tension is applied to the beam in a nonlinear static load case that is specified to consider P-Delta effects. The beam is then analyzed in a separate linear static load case with the transverse loading applied. This second load case is specified to use the stiffness at the end of the static nonlinear case.
The beam is modeled with two objects so that there is a midpoint node where displacements are reported. Several models are created using different discretizations of the frame objects
Important Note: Shear deformations are ignored in the analysis by setting the frame property modification factor for shear area to zero.

Tested Features

P-Delta force assignment to frame objects
Nonlinear static analysis using the P-Delta option
Automatic frame subdivision

App

Object Link: https://openbrim.org/objid9tn6bq2wb4s6nigzi3pptn.project

Library

Object Link: https://openbrim.org/objidl060eu5ou4k6utlm8t2yk.libobj

Without Tension Stiffening

Model

# Elm

Output Parameter

OpenBrIM

SAP2000

Independent

Percent Difference

(SAP2000 vs Independent)

Percent Difference

(OpenBrIM vs Independent)

A

1

Uz (midpt) in

−1.04167

-1.04167

-1.04167

0%

0%

My (midpt) k-in

22.500

22.500

22.500

0%

0%

With Tension Stiffening - Using P-Delta Force Method

Model	# Elm	Output Parameter	OpenBrIM	SAP2000	Independent	Percent Difference (SAP2000 vs Independent)	Percent Difference (OpenBrIM vs Independent)
B	1	Uz (jt 2) in	-0.5995	-0.54555	-0.54330	0.41%	7.84%
B	1	My (jt1) k-in	12.6631	11.453	11.498	-0.39%	6.36%
C	2	Uz (jt 2) in	-0.5696	-0.54343	-0.54330	0.02%	3.73%
C	2	My (jt 1) k-in	12.0938	11.495	11.498	-0.03%	4.37%
D	16	Uz (jt 2) in	-0.568	-0.54330	-0.54330	0%	4.01%
D	16	My (jt 1) k-in	12.0518	11.498	11.498	0%	4.44%

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