A two-span beam is supported at an interior point by a column and with yielding elastic supports at the two exterior points. The beam is continuous and the column is pin-connected to the beam.

The beam is subjected to a vertical point load and the column is subjected to a horizontal point load. Determine the deflections and reactions.

The 2D model consists of 6 joints, 3 beam elements and 2 spring elements. This is a plane frame analysis. The translational displacement in Global Y-direction and rotations about Global X and Z-directions can be deleted from the analysis. The joints 1, 4 and 6 are fixed supports.

The material property data is given:

Modulus of Elasticity = 30,000,000 psi

and sectional property data:

Area = 0.125 ft2

Izz = 0.263 ft4 for beams

Area = 0.175 ft2

Izz = 0.193 ft4 for columns

The spring constant for the springs is given as:

k = 1200 kip/ft

The member loads applied on beams are:

P = -15 kips on beam # 2 @ mid-span in Global Y

P = -5 kips on beam #3 @ mid-span in Global X

Linear static analysis with one load case is performed.

Tested Features

App

Object Link: https://openbrim.org/objid65tv28lznd34ie4efzje1.project

Library

Object Link: https://openbrim.org/objidi4segrgj8hdgrq97j7q0w.libobj

Sources

Beaufait, F.W., et al., "Computer Methods of Structural Analysis," Prentice-Hall, 197-210.
LARSA 4D

Result Comparison

Output Parameters	Independent (Beaufait)	Larsa	OpenBrIM	Percent Difference (Larsa vs Independent)	Percent Difference (OpenBrIM vs Independent)
U2 (x10^-3 ft)	0.013	0.013	0.013	0%	0%
U3 (x10^-3 ft)	0.013	0.013	0.013	0%	0%
U5 (x10^-3 ft)	0.013	0.013	0.013	0%	0%
V2 (x10^-3 ft)	0.021	0.021	0.021	-0.017%	0%
V3 (x10^-3 ft)	-0.002	-0.002	-0.002	0%	0%
V5 (x10^-3 ft)	-0.058	-0.058	-0.058	0.004%	0%
R2 (x10^-3 rad)	0.000	0.000	0.000	0%	0%
R3 (x10^-3 rad)	-0.000	-0.000	0.000	0%	0%
R5 (x10^-3 rad)	0.000	0.000	0.000	0%	0%
Reaction V @ Joint 1 (kip)	-2.1	-2.144	-2.144	2.095%	2.052%
Reaction H @ Joint 4 (kip)	-5.0	-5.0	-5.0	0%	0%
Reaction V @ Joint 4 (kip)	11.3	11.360	11.360	0.531%	0.531%
Reaction M @ Joint 4 (kip)	-360	-360	-360	0%	0%
Reaction V @ Joint 6 (kip)	5.8	5.7845	5.8	-0.267%	0%

U denotes the displacement in horizontal direction and V denotes the displacement in vertical direction. R is the rotation. Reaction V is the vertical force at the support joint and Reaction H is the horizontal force. Reaction M is the support moment.

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