V.热荷载下电缆中的应力

一根刚性杆由两根铜线和一根钢线悬挂。求由于温度升高导致的线中应力。

References

Timoshenko, S., Strength of Materials, 第 1 部分, D. Van Nostrand Co., 第 3 版, 1956, 第 30 页, 问题 9.

Details

假设水平构件非常刚性，确定如果温度升高 10°F 时铜线和钢线中的应力。构件 1 和 3 是铜，构件 2 是钢。

Esteel = 30×(10)6 psi, Ecopper = 16×(10)6 psi
αsteel = 70E-7 in/in/°F,  αcopper = 92E-7 in/in/°F
AX = 0.1 in2
w = 400 lbf/in.
L = 20 in.d= 5 in.
Figure 1. 由线悬挂的刚性杆模型

Results

Table 1. 结果比较
结果类型 理论 STAAD.Pro 差异
σSteel (psi) 19,695 19,698.3 可忽略
σCopper (psi) 10,152 10,150.8 可忽略

Input

文件 C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\01 Beams\Stresses in a Cable due to Thermal Loading.STD 通常随程序安装。

STAAD

STAAD PLANE :A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL WIRE
START JOB INFORMATION
ENGINEER DATE 09-Oct-17
END JOB INFORMATION
*
*  REFERENCE: 'STRENGTH OF MATERIALS', TIMOSHENKO (PART 1),
*              PAGE 30, PROB 9.
*              THE ANSWERS ARE 19700 PSI AND 10200 PSI.
*
UNIT INCHES POUND
JOINT COORDINATES
1 0 20 0; 2 5 20 0; 3 10 20 0; 4 0 0 0; 5 5 0 0; 6 10 0 0;
MEMBER INCIDENCES
1 1 4; 2 2 5; 3 3 6; 4 4 5; 5 5 6;
MEMBER PROPERTY AMERICAN
1 TO 3 PRIS AX 0.1 IZ 0.0001
4 5 PRIS AX 1 IZ 100
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 1.6e+007
POISSON 0.230769
ALPHA 9.2e-006
ISOTROPIC MATERIAL2
E 3e+007
POISSON 0.290909
ALPHA 7e-006
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 MEMB 1 3
MATERIAL MATERIAL2 MEMB 2 4 5
SUPPORTS
1 2 3 Fixed
MEMBER RELEASE
1 TO 3 START MPZ 0.99
1 TO 3 END MZ
LOAD 1 VERT LOAD + TEMP LOAD
MEMBER LOAD
4 5 UNI Y -400
TEMPERATURE LOAD
1 TO 3 TEMP 10
PERFORM ANALYSIS
PRINT MEMBER STRESSES LIST 1 TO 3
FINISH

Output

  MEMBER STRESSES
  ---------------
  ALL UNITS ARE POUN/SQ INCH
 MEMB   LD  SECT    AXIAL    BEND-Y     BEND-Z   COMBINED  SHEAR-Y  SHEAR-Z
      1    1   .0  10150.8 T      0.0       0.0   10150.8      0.0      0.0 
              1.0  10150.8 T      0.0       0.0   10150.8      0.0      0.0
      2    1   .0  19698.3 T      0.0       0.0   19698.3      0.0      0.0 
              1.0  19698.3 T      0.0       0.0   19698.3      0.0      0.0
      3    1   .0  10150.8 T      0.0       0.0   10150.8      0.0      0.0