MEC 2213 Engineering

Solid Mechanics

CHAPTER: AXIAL LOADING - STRESS & STRAIN

TRUE STRESS AND TRUE STRAIN

Since the cross-sectional area of the specimen decreases as P increases, the stress plotted in our diagrams does not represent the actual stress in the specimen.

Engineering Stress

True Stress

Obtained by dividing P by the cross-sectional area A of the deformed specimen becomes apparent in ductile materials after yield has started.

TRUE STRESS AND TRUE STRAIN

Figure 2.19a

Axial Loading

Example

Figure 2.19a

Two prismatic bars are rigidly fastened together and support a vertical load of 45 kN, as shown in Figure. !The upper bar is steel having length 10 m and cross-sectional area 60 cm2. The lower bar is brass having length 6 m and cross-sectional area 50 cm2. !For steel E = 200 GPa, for brass E = 100 GPa. Determine the maximum stress in each material.

Figure 2.21a

Question

Consider a steel tube surrounding a solid aluminum cylinder, the assembly being compressed between rigid cover plates by centrally applied forces as shown in Figure. "!The aluminum cylinder is 8 cm in diameter and the outside diameter of the steel tube is 9.2 cm. If P = 200 kN, find the stress in the steel and also in the aluminum. "!For steel, E = 200 GPa and for aluminum E = 80 GPa.

Question

Question

A steel bolt, 2.50 cm in diameter, carries a tensile load of 40 kN. Estimate the average tensile stress at the section a and at the screwed section b, where the diameter at the root of the thread is 2.10 cm.

Question