Page 23 - Marks Calculation for Machine Design

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January 4, 2005
Brown.cls
Brown˙C01
U.S. Customary FUNDAMENTAL LOADINGS SI/Metric 5
Example 1. Determine the normal stress in a Example 1. Determine the normal stress in a
square bar with side (a) loaded in tension with square bar with side (a) loaded in tension with
forces (P), where forces (P), where
P = 12 kip = 12,000 lb P = 55 kN = 55,000 N
a = 2in a = 5cm = 0.05 m
solution solution
Step 1. Calculate the cross-sectional area (A) Step 1. Calculate the cross-sectional area A of
of the bar. the bar.
2
2
2
2
A = a = (2in) = 4in 2 A = a = (0.05 m) = 0.0025 m 2
Step 2. From Eq. (1.1), calculate the normal Step 2. From Eq. (1.1), calculate the normal
stress (σ) in the bar. stress (σ) in the bar.
P 12,000 lb P 55,000 N
σ = = σ = =
A 4in 2 A 0.0025 m 2
2
2
= 3,000 lb/in = 3.0 kpsi = 22,000,000 N/m = 22 MPa
Example 2. Calculate the minimum cross- Example 2. Calculate the minimum cross-
sectional area (A min ) needed for a bar axially sectional area (A min ) needed for a bar axially
loaded in tension by forces (P) so as not to ex- loaded in tension by forces (P) so as not to ex-
ceed a maximum normal stress (σ max ), where ceed a maximum normal stress (σ max ), where
P = 10 kip = 10,000 lb P = 45 kN = 45,000 N
σ max = 36,000 psi σ max = 250 MPa
solution solution
Step 1. Start with Eq. (1.1) where the normal Step 1. Start with Eq. (1.1) where the normal
stress (σ) is maximum and the area (A) is min- stress (σ) is maximum and the area (A) is min-
imum to give imum to give
P P
σ max = σ max =
A min A min
Step 2. Solve for the minimum area (A min ). Step 2. Solve for the minimum area (A min ).
P P
A min = A min =
σ max σ max
Step 3. Substitute for the force (P) and the Step 3. Substitute for the force (P) and the
maximum normal stress. maximum normal stress.
10,000 lb 2 45,000 N 2
A min = = 0.28 in A min = = 0.00018 m
6
36,000 lb/in 2 250 × 10 N/m 2

Strain. The axial loading shown in Fig. 1.6 also produces an axial strain (ε), given by
Eq. (1.2).

δ
ε = (1.2)
L
where (δ) is change in length of the bar and (L) is length of the bar.