1. Stress Concentrations
Lecture # 9
Stress Concentrations
Objective:
To find stress within a member
of abrupt change in shape.

2. Stress Concentrations Factors

3. Figure:

4. Figure:

5. Example:
A steel bar has the dimensions as shown in figure. If the allowable stress is allow = 115 MPa, determine the largest axial force P that the bar can carry.

6. Solution:
Because there is a shoulder fillet, the stress-concentration factor can be determined using the graph as in the previous figure. Calculating the necessary geometric parameters yields
Thus, from the graph,
K = 1.4

7. Solution:
Computing the average normal stress at the smallest cross-section,
we have
Applying equation with allow = max yield
allow = Kavg
115 N/mm2 = 1.4(0.005 P)
P = (103) N Ans…..
= kN

8. Problem:
Determine the maximum normal stress developed in the bar when it is subjected to a tension of P = 8 kN.
If the allowable normal stress for the bar is allow = 120 MPa, determine the maximum axial force P that can be applied to the bar.

9. Solution:

10. Solution:

11. The enD