Stress Analysis
Mech 422 - Stress and
Strain Analysis
D.L. DuQuesnay
(adapted from original text by R.J. Ferguson)
z
R
σ xz
1
σ zz
σ zx σ xx
x
September 2002
σ yz
R
σ zy σ yx σ xy σ yy
y
2
Chapter 1
Introduction
1.
What is Stress Analysis?
The aim of stress analysis is to take the geometry of a component or structure and the externally applied “loads” and determine the state of stress in the material. Subjects that encompass stress analysis include “strength of materials”, “solid mechanics”, mechanics of deformable solids” , etc. When the stresses in the body are known, the material properties are used in a failure theory to decide whether the body can withstand the design loads. If this is the case, then further analysis may be undertaken to determine the service life of the structure. In general, these analyses are accomplished by computation with a calculator or a computer. However, stress analysis may also be performed experimentally. Since the computer has invaded the design office, the importance of experimental stress analysis has waned in recent times. It is now mainly used in the determination of loads and stresses for in-service components or systems.
The following definitions are important:
2.
•
Stress analysis: used to find the stresses in a loaded body.
•
Exact solution: is one that satisfies the conditions of equilibrium, compatibility and meets the boundary conditions of the body and its loads. There are comparatively few exact solutions in stress analysis.
•
Closed-form solution: involves mathematical relationships that can be manipulated by the ordinary operations of algebra and calculus to determine the stresses. Many closed-form solutions involve simplifying assumptions that may make the results invalid for some situations or for portions of a loaded body.
•
Numerical solution: uses algorithms for equations that cannot be solved easily
(or at all) by conventional algebraic means.
•
Finite element method: is a computer-based method
Strain Analysis
D.L. DuQuesnay
(adapted from original text by R.J. Ferguson)
z
R
σ xz
1
σ zz
σ zx σ xx
x
September 2002
σ yz
R
σ zy σ yx σ xy σ yy
y
2
Chapter 1
Introduction
1.
What is Stress Analysis?
The aim of stress analysis is to take the geometry of a component or structure and the externally applied “loads” and determine the state of stress in the material. Subjects that encompass stress analysis include “strength of materials”, “solid mechanics”, mechanics of deformable solids” , etc. When the stresses in the body are known, the material properties are used in a failure theory to decide whether the body can withstand the design loads. If this is the case, then further analysis may be undertaken to determine the service life of the structure. In general, these analyses are accomplished by computation with a calculator or a computer. However, stress analysis may also be performed experimentally. Since the computer has invaded the design office, the importance of experimental stress analysis has waned in recent times. It is now mainly used in the determination of loads and stresses for in-service components or systems.
The following definitions are important:
2.
•
Stress analysis: used to find the stresses in a loaded body.
•
Exact solution: is one that satisfies the conditions of equilibrium, compatibility and meets the boundary conditions of the body and its loads. There are comparatively few exact solutions in stress analysis.
•
Closed-form solution: involves mathematical relationships that can be manipulated by the ordinary operations of algebra and calculus to determine the stresses. Many closed-form solutions involve simplifying assumptions that may make the results invalid for some situations or for portions of a loaded body.
•
Numerical solution: uses algorithms for equations that cannot be solved easily
(or at all) by conventional algebraic means.
•
Finite element method: is a computer-based method