ENGR 220Section 4.7

Saint-Venant’s Principle

• When loading is applied at a point on a body, it tends to create a stress distribution that becomes more uniform at regions removed from the point of application.

Stiffeners are welded to corners to mitigate stress concentrations.

Stress Concentration Factor, K

avg

max

K

area. sectional-crosssmallest theis where,avg AA

P

Stress Concentration Factor

Stress Concentration Factor

Important Points

• Stress concentrations occur at sections where the cross-sectional area suddenly changes. The more severe the change the larger the stress concentration

Important Points

• For design or analysis it is only necessary to determine the maximum stress acting on the smallest cross sectional area.

Important Points

• Normally the stress concentration in a ductile material that is subjected to static loading will not have to be considered in a design. If the material is brittle or subjected to fatigue loadings, then stress concentrations become important.

http://upload.wikimedia.org/wikipedia/commons/3/38/Stress.JPG

THE ROLE OF STRESS CONCENTRATION INSLAB AVALANCHE RELEASE

By R. A. SOMMERFELD

U.S. Forest Service, Rocky Mountain Forest and Range Experiment Station, Fort Collins, Colorado 80521, U.S.A. ~1967

ABSTRACT

Slab avalanches are shown to be released by brittle fracture. An analogy is drawn in which the snow- pack is considered to be a macroscopic, molecular model of glass. The analogy is examined qualitatively from two viewpoints: the Griffith fracture criterion, and stress concentration theory. The details of fracture propagation in a layered snow-pack are explained by means of stress concentration theory, and many details of slab avalanches are shown to be consistent with the proposed mechanism. The significance of various fracture surface markings is pointed out.

Lecture Example: Determine the maximum normal stress developed in the bar when it is subjected to a tension of P=2 kip.