V. Hanging Bar Axial Stress

Two vertical bars are supported by a rigid bar, which is pinned-supported on one end. Find stresses in vertical bars due to a load at the free end of the rigid bar.

Reference

Higdon, Ohlsen, Stiles, Weese and Riley, Mechanics of Materials, 3rd Edition, John Wiley & Sons, Page 135, Problem 3-37.

Problem

TBars A and B are connected by rigid links to a fixed support at the top and to a rigid bar at the bottom. Determine the axial stresses in bars A and B when the load P is 177.92888 kN applied as shown.

P = 177.93 kN

A_A = 1,290.3 mm²

A_B = 1,612.9 mm²

E_A = 68.95 GPa

E_B = 206.84 GPa

Assume the moment of inertia of member CD to be very large.

Rigid bar hanging from a pair of rods

Comparison

Table 1. Comparison of results
Result Type	Theory	STAAD.Pro	Difference
Stress in A (GPa)	0.17237	0.1723889	negligible
Stress in B (GPa)	0.20684	0.2068032	negligible

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\01 Beams\Hanging Bar Axial Stress.STD is typically installed with the program.

STAAD PLANE :TWO VERTICAL MEMBERS SUPPORT A RIGID BAR
START JOB INFORMATION
ENGINEER DATE 18-Sep-18
END JOB INFORMATION
*
* REFERENCE: MECHANICS OF MATERIALS, HIGDON, OHLSEN, STILES, WEESE
*            AND RILEY, 3RD EDITION, JOHN WILEY &amp; SONS,
*            PAGE 135, PROBLEM 3-37
*
UNIT METER NEWTON
JOINT COORDINATES
1 0 0 0; 2 0.127 0 0; 3 0.2032 0 0; 4 0.254 0 0; 5 0.127 0.254 0;
6 0.2032 0.254 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 3 6;
MEMBER PROPERTY AMERICAN
1 TO 3 PRIS AX 0.032258 IZ 0.00208226
4 PRIS AX 0.00129032
5 PRIS AX 0.0016129
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 2.06843e+08
POISSON 0.290909
ISOTROPIC MATERIAL2
E 6.89477e+07
POISSON 0.329996
END DEFINE MATERIAL
UNIT METER NEWTON
CONSTANTS
MATERIAL MATERIAL1 MEMB 1 TO 3 5
MATERIAL MATERIAL2 MEMB 4
MEMBER TRUSS 
4 5
SUPPORTS
4 PINNED
5 6 FIXED
LOAD 1 VERTICAL JOINT LOAD
JOINT LOAD
1 FY -177929
PERFORM ANALYSIS
UNIT METER KN
PRINT MEMBER STRESSES LIST 4 5
FINISH

STAAD Output

  MEMBER STRESSES
  ---------------
  ALL UNITS ARE KN  /SQ METE
 MEMB   LD  SECT    AXIAL    BEND-Y     BEND-Z   COMBINED  SHEAR-Y  SHEAR-Z
      4    1   .0 172388.9 T      0.0       0.0  172388.9      0.0      0.0
              1.0 172388.9 T      0.0       0.0  172388.9      0.0      0.0
      5    1   .0 206803.2 T      0.0       0.0  206803.2      0.0      0.0
              1.0 206803.2 T      0.0       0.0  206803.2      0.0      0.0