Page 88 - 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 ) Example 2. Calculate the shear force (V )
and bending moment (M) for a simply- and bending moment (M) for a simply-
supported beam of length (L) with twin con- supported beam of length (L) with twin con-
centrated forces, both of magnitude (F) and centrated forces, both of magnitude (F) and
located equidistant from the supports, at a located equidistant from the supports, at a
distance (x), where distance (x), where
F = 1,000 lb F = 4,500 N
L = 5 ft, a = 1ft L = 1.5 m, a = 0.3 m
x = 2ft x = 0.5 m
solution solution
Step 1. Note that the distance (x) of2ftis Step 1. Note that the distance (x) of 0.5 m is
between the two forces. between the two forces.
a ≤ x ≤ L − a or 1 ft ≤ 2ft ≤ 4ft a ≤ x ≤ L − a or 0.3m ≤ 0.5m ≤ 1.2m
Step 2. Determine the shear force (V ) for the Step 2. Determine the shear force (V ) for the
distance (x) from Fig. 2.48 as distance (x) from Fig. 2.48 as
V = 0 V = 0
Step 3. Determine the bending moment (M) Step 3. Determine the bending moment (M)
for the distance (x) from Eq. (2.31b). for the distance (x) from Eq. (2.31b).
M = Fa = (1,000 lb)(1ft) M = Fa = (4,500 N)(0.3m)
= 1,000 ft · lb = 1,350 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 = 1,000 lb F = 4,500 N
L = 5 ft, a = 1ft L = 1.5 m, a = 0.3 m
solution solution
Step 1. Calculate the maximum shear force Step 1. Calculate the maximum shear force
(V max ) from Eq. (2.30) as (V max ) from Eq. (2.30) as
V max = F = 1,000 lb V max = F = 4,500 N
Step 2. Fig. 2.48 shows that the maximum Step 2. As shown in Fig. 2.48 the maximum
shear force (V max ) occurs in two regions: one shear force (V max ) occurs in two regions, one
from the left end of the beam to the first con- from the left end of the beam to the first con-
centrated force, and the other from the second centrated force, and the other from the second
concentrated force to the right end of the beam. concentrated force to the right end of the beam.
Step 3. Calculate the maximum bending Step 3. Calculate the maximum bending
moment (M max ) from Eq. (2.32). moment (M max ) from Eq. (2.32).
M max = Fa = (1,000 lb)(1ft) M max = Fa = (4,500 N)(0.3m)
= 1,000 ft · lb = 1,350 N · m
Step 4. From Fig. 2.49 we see that the max- Step 4. From Fig. 2.49 we see that the max-
imum bending moment (M max ) occurs in the imum bending moment (M max ) occurs in the
region between the two forces. region between the two forces.