V. Bent Cantilever Deflection

Find deflection due to load at the free end of a cantilever plane bent.

Reference

Kinney, J. S., Indeterminate Structural Analysis, Addison - Wesley Publishing Co., 1957, Page 13, Problem 4 - 38.

Problem

Find the vertical, horizontal and rotational deflection components of point A.

E = 30,000 ksi

I = 200 in⁴

A = 10 in²

Bent plate frame

Comparison

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
Deflection right, δ_x (in)	0.53	0.53056	none
Deflection down, δ_y (in)	1.16	-1.17109	<1%
Rotation, θ (rad)	0.0049	0.00488	none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Bent Cantilever Deflection.STD is typically installed with the program.

STAAD PLANE :A CANTILEVER PLANE BENT
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: INDETERMINATE STRUCTURAL ANALYSIS, KINNEY, 1957,
*    ADISON-WESLEY PUBLISHING CO., PAGE 113, PROBLEM 4-38
*
UNIT FEET KIP
JOINT COORDINATES
1 0 3 0; 2 0 0 0; 3 4 0 0; 4 14 10 0; 5 22 10 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 5;
UNIT INCHES KIP
MEMBER PROPERTY AMERICAN
1 TO 4 PRIS AX 10 IZ 200
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 30000
POISSON 0.290909
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
5 FIXED
LOAD 1 HORIZONTAL JOINT LOAD
JOINT LOAD
1 FX 3
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 1
FINISH

STAAD Output

   JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = PLANE
   ------------------
 JOINT  LOAD   X-TRANS   Y-TRANS   Z-TRANS   X-ROTAN   Y-ROTAN   Z-ROTAN
      1    1    0.53056  -1.17109   0.00000   0.00000   0.00000   0.00488