# Solid Mechanic

Topics: Elasticity, Stress concentration, Fatigue Pages: 16 (2276 words) Published: May 18, 2013
Chapter Objectives
  To determine the deformation of axially loaded members. To determine the support reactions when these reactions cannot be determined solely from the equations of equilibrium. To analyze the effects of thermal stresses. Copyright © 2011 Pearson Education South Asia Pte Ltd

In-class Activities
1. 2. 3. 4. 5. 6. 7. 8. 9. Reading Quiz Applications Elastic deformation in axially loaded member Principle of superposition Compatibility conditions ‘Force method’ of analysis Thermal Stress Stress Concentration Concept Quiz

1) The stress distributions at different cross sections are different. However, at locations far enough away from the support and the applied load, the stress distribution becomes uniform. This is due to a) b) c) d) Principle of superposition Inelastic property Poisson’s effect Saint Venant’s Principle

2) The principle of superposition is valid provided that
1. 2. 3. 4. a) b) c) d) The loading is linearly related to the stress or displacement The loading does not significantly change the original geometry of the member The Poisson’s ratio v ≤ 0.45 Young’s Modulus is small a, b and c a, b and d a and b only All Copyright © 2011 Pearson Education South Asia Pte Ltd

3) The units of linear coefficient of thermal expansion are
a) b) c) d) per ° C per ° F per ° K (Kelvin) all of them

4) Stress concentrations become important in design if

d)

All of them

5) The principle of superposition is applicable to
a) b) c) d) inelastic axial deformation residual stress evaluation large deformation None of the above

APPLICATIONS

Most concrete columns are reinforced with steel rods; and these two materials work together in supporting the applied load. Are both subjected to axial stress?

APPLICATIONS (cont)
Thermal Stress Stress Concentration Inelastic Axial Deformation

ELASTIC DEFORMATION OF AN AXIALLY LOADED MEMBER

P x  dδ and ε  Ax  dx

Provided these quantities do not exceed the proportional limit, we can relate them using Hooke’s Law, i.e. ζ = E ε Px   d   E  A x   dx  P x dx d  A x E P x dx   A x E 0 L

EXAMPLE 1
The assembly shown in Fig. 4–7a consists of an aluminum tube AB having a cross-sectional area of 400 mm2. A steel rod having a diameter of 10 mm is attached to a rigid collar and passes through the tube. If a tensile load of 80 kN is applied to the rod, determine the displacement of the end C of the rod. Take Est = 200 GPa, Eal = 70 GPa.

EXAMPLE 1 (cont)
Solution
• Find the displacement of end C with respect to end B.
C / B
PL  80103  0.6    0.003056 m  AE  0.005 200109 

• Displacement of end B with respect to the fixed end A,
PL  80103  0.4 B    0.001143  0.001143 m  AE 400106  70109 



• Since both displacements are to the right,  C   C   C / B  0.0042 m  4.20 mm 

EXAMPLE 2
A member is made from a material that has a specific weight and modulus of elasticity E. If it is in the form of a cone having the...