Page 62 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
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U.S. Customary 16:18 STRENGTH OF MACHINES SI/Metric
Example 2. Calculate the shear force (V ) and Example 2. Calculate the shear force (V ) and
bending moment (M) for a simply-supported bending moment (M) for a simply-supported
beam with a concentrated force (F) at an inter- beam with a concentrated force (F) at an inter-
mediate point a distance (L/2), where mediate point a distance (L/2), where
F = 10 kip = 10,000 lb F = 45 kN = 45,000 N
L = 8 ft, a = 6 ft, b = 2ft L = 3m, a = 2m, b = 1m
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 8ft L 3m
x = = = 4ft x = = = 1.5m
2 2 2 2
Step 2. Determine the shear force (V ) from Step 2. Determine the shear force (V ) from
Fig. 2.20 as Fig. 2.20 as
Fb (10,000 lb)(2ft) Fb (45,000 N)(1m)
V = = V = =
L 8ft L 3m
20,000 ft · lb 45,000 N · m
= = 2,500 lb = = 15,000 N
8ft 3m
Step 3. Determine the bending moment (M) Step 3. Determine the bending moment (M)
from Eq. (2.7a). from Eq. (2.7a).

Fb (10,000 1b)(2ft) Fb (45,000 N)(1m)
M = x = (4ft) M = x = (1.5m)
L 8ft L 3m
20,000 ft · lb 45,000 N · m
= (4ft) = (1.5m)
8ft 3m
= (2,500 lb)(4ft) = 10,000 ft · lb = (15,000 N)(1.5m) = 22,500 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
F = 10 kip = 10,000 lb F = 45 kN = 45,000 N
L = 8 ft, a = 6 ft, b = 2ft L = 3m, a = 2m, b = 1m
solution solution
Step 1. Calculate the maximum shear force Step 1. Calculate the maximum shear force
(V max ) from Eq. (2.6) as (V max ) from Eq. (2.6) as
Fa (10,000 lb)(6ft) Fa (45,000 N)(2m)
V max = = V max = =
L 8ft L 3m
60,000 ft · lb 90,000 N · m
= = 7,500 lb = = 30,000 N
8ft 3m
Step 2. As shown in Fig. 2.20 this maximum Step 2. As shown in Fig. 2.20, this maximum
shear force (V max ) of 7,500 lb occurs in the re- shear force (V max ) of 30,000 N occurs in the
gion between where the force (F) acts and the region between where the force (F) acts and
right end of the beam. the right end of the beam.