Page 82 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
64
U.S. Customary 16:18 STRENGTH OF MACHINES SI/Metric
solution solution
Step 1. Establish the distance (x) from the left Step 1. Establish the distance (x) from the left
end of the beam, where end of the beam, where
L 6ft L 1.8m
x = = = 2ft x = = = 0.6m
3 3 3 3
Step 2. Determine the shear force (V ) from Step 2. Determine the shear force (V ) from
Eq. (2.24) as Eq. (2.24) as

2 2
wL x wL x
V = 1 − 3 V = 1 − 3
6 L 6 L

lb N
750 (6ft)
2 10,000 (1.8m)
2
ft 2ft m 0.6m
= 1 − 3 = 1 − 3
6 6ft 6 1.8m
4,500 lb 18,000 N
= [1 − 0.333] = [1 − 0.333]
6 6
= (750 lb)(0.677) = (3,000 N)(0.677)
= 500 lb = 2,000 N
Step 3. Determine the bending moment (M) Step 3. Determine the bending moment (M)
from Eq. (2.26). from Eq. (2.26).

2
2
wLx x wLx x
M = 1 − M = 1 −
6 L 6 L
lb N

750 (6ft)(2ft)
2 10,000 (1.8m)(0.6m)
2
ft 2ft m 0.6m
= 1 − = 1−
6 6ft 6 1.8m
9,000 ft · lb 10,800 N · m
= [1 − 0.111] = [1 − 0.111]
6 6
= (1,500 ft · lb)(0.889) = (1,800 N · m)(0.889)
= 1,333 ft · lb = 1,600 N · m
Example 3. Calculate and locate the max- Example 3. Calculate and locate the max-
imum shear force (V max ) and the maximum imum shear force (V max ) and the maximum
bending moment (M max ) for the beam of bending moment (M max ) for the beam of
Examples 1 and 2, where Examples 1 and 2, where
w = 750 lb/ft w = 10,000 N/m
L = 6ft L = 1.8 m
solution solution
Step 1. Calculate the maximum shear force Step 1. Calculate the maximum shear force
(V max ) from Eq. (2.25) as (V max ) from Eq. (2.25) as
wL (750 lb/ft)(6ft) wL (10,000 N/m)(1.8m)
V max = = V max = =
3 3 3 3
4,500 lb 18,000 N
= = 1,500 lb = = 6,000 N
3 3
Step 2. Figure 2.41 shows that this maximum Step 2. Figure 2.41 shows that this maximum
shear force (V max ) of 1,500 lb occurs at the right shear force (V max ) of 6,000 N occurs at the right
end of the beam. end of the beam.