V. Tee Shaped Cantilever

To find the stress due to an applied moment at the free end of a cantilever beam with inverted tee section.

Reference

Hand calculation using the following reference:

Crandall, S.H., and Dahl, N.C., An Introduction to the Mechanics of Solids, McGraw-Hill, Inc., 1959, Page 294, Problem 7.2..

Problem

Find the maximum bending stress in the beam of length L with due to moment, M, and the free end.

E = 30×(10)⁶ psi

L = 10 in.

M = 1,000,000 in.·lb.

Cross section of cantilever beam

Comparison

Table 1. Comparison of results
Result	Theory	STAAD.Pro	Difference
Bending stress, σ (psi)	700	700	none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Tee Shaped Cantilever.STDis typically installed with the program.

STAAD PLANE :A CANTILEVERED BEAM OF INVERTED TEE SECTION
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: CRANDALL &amp; DAHL, AN INTRODUCTION TO THE MECHANICS
*            OF SOLIDS, PAGE294, EX. 7.2
*
INPUT WIDTH 79
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 10 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 PRIS YD 20 ZD 9 YB 16 ZB 1.5
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.290909
END DEFINE MATERIAL
CONSTANTS
BETA 180 ALL
MATERIAL MATERIAL1 ALL
SUPPORTS
1 FIXED
LOAD 1 CONSTANT MOMENT
JOINT LOAD
2 MZ 100000
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT MEMBER STRESSES ALL
FINISH

STAAD Output

  ALL UNITS ARE POUN/SQ INCH
 MEMB   LD  SECT    AXIAL    BEND-Y     BEND-Z   COMBINED  SHEAR-Y  SHEAR-Z
      1    1   .0      0.0        0.0     700.0     700.0      0.0      0.0
              1.0      0.0 C      0.0     700.0     700.0      0.0      0.0