Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

1

Chapter 2:Stress, Strain, Axial Loading

Stress – Strain RelationshipDeformation in Axial Load StructuresYoung’s Modulus/Modulus of Elasticity

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

2

Consider Affect of Geometry

strain normal

stress

==

==

L

AP

δε

σ

L

AP

AP

δε

σ

=

==22

LL

AP

δδε

σ

==

=

22

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

3

Load Displacement Curves

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

4

Relationship Between Stress and Strain in Ductile Materials

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

5

Relationship Between Stress and Strain in Brittle Materials

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

6

Behavior of Materials

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

7

Axial Loading and Deformation

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

8

Consider Multiple Steps

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

9

Loading in Non-Prismatic Cross-Section

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

10

Example 1Given the rod shown, it has been reported that under this loading condition the rod has extended a total of 0.1524mm.

Determine the stress in sections a-b and b-cDetermine the strain in sectins a-b and b-c

Ronald B. Bucinell, Ph.D., P.E. MER214: Strength of MaterialsDepartment of Mechanical Engineering

Union College, Schenefctady, NY

11

Example 2Determine the elongation in this two force member under compressive loading given E=200GPa