Calculating Strain and Stress in a Steel Plate Under Tensile Load

[fnicolep92]

Homework Statement

A 2.75 KN tensile load is applied to at test coupon made from 1.6 mm flat steel plate (E=200 GPa, v=0.30). Determine the resulting change in the 50 mm gage length.

Homework Equations

ε_x = (σ_x/E) + (-Vσ_y/E) - (Vσ_z/E)
ε_y = (-vσ_x/E) + (σ_y/E) - (Vσ_z/E)
ε_z = (-vσ_x/E) - (Vσ_y/E) + (σ_z/E)

The Attempt at a Solution

(a) Area = (0.05)(0.0016) = 0.00008 m²
σ_x = P/A = (2.75*10³) / 0.00008
σ_x = 34.4*10⁶ Pa

ε_x = (34.4*10⁶) / (200*10⁹)
ε_x = 1.719*10^-4

Δab = ε_x(ab) = (1.719*10^-4 / 0.05
Δab = 8.595*10^-6

The answer should be 0.0358 mm. What am I doing wrong?

 

[Chestermiller]

For one thing, your cross sectional area is 1.6x12, not 1.6x50. Also, you should be multiplying by 50 in getting Δab, not 0.05.

Chet