The tool SM-13 computes the internal force and stress in bars due to fabrication errors and thermal effects.
In addition, a tutorial on how to use the tool in computation is provided and a subject review on fundamental theories and useful formulas is presented.
Example: Stress in bar by thermal effects
The input in the tool is
After clicking "Run", the results will be shown as follows in another page.
Change in length, ΔL = α*ΔT*L = 5.0000E-8
Stress in the bar, σ = E*α*ΔT = -85.000E-4
Inernal force on a cross section of the bar, P = E*α*ΔT*A = -85.000E-6
(Positive (+): Tensile; Negative (-): Compressive)
Due to fabrication errors and thermal effects, a bar may be subject to changes in length, which in return can cause elastic deformation of the bar.
(a) Too long
(a) Too short
Fig. 1 Fabrication error
If the bar is manufactured too long by an amount ΔL, as shown in Fig. 1a, it will cause a compression internal force. On the other hand, if the bar is too short, a tension internal force will be caused. Both the tension and compression stress is given by
E: Young's modulus
A: Area of the cross-section
L: Length of the bar
And the internal force P is in the form of
If a bar of length L subject to a temperature increase ΔT, it will undergo an increase in length
α: Coefficient of thermal expansion
If the boundary condition of the bar is fixed-fixed, the internal stress is determined by
For the boundary condition fixed-spring or spring-fixed, the internal stress is
If both boudanries are springs, the internal stress is given by
1. Yang, B., 2005, Stress, Strain, and Structural Dynamics: An Interactive Handbook of Formulas, Solutions, and MATLAB Toolboxes, Elsevier Science.
2. Young, W.C., 1989, Roark's Formulas for Stress and Strain, 6th edition, McGraw-Hill, New York.