Page 76 - 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
Step 3. Determine the bending moment (M) Step 3. Determine the bending moment (M)
from Eq. (2.20). from Eq. (2.20).
wx wx
M = (L − x) M = (L − x)
2 2

lb N
400 (5ft) 6,000 (1.5m)
ft m
= (15 ft − 5ft) = (5m − 1.5m)
2 2
2,000 lb 9,000 N
= (10 ft) = (3.5m)
2 2
= (1,000 lb)(10 ft) = 10,000 ft · lb = (4,500 N)(3.5m) = 15,750 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 = 400 lb/ft w = 6,000 N/m
L = 15 ft L = 5m
solution solution
Step 1. Calculate the maximum shear force Step 1. Calculate the maximum shear force
(V max ) from Eq. (2.19) as (V max ) from Eq. (2.19) as
wL (400 lb/ft)(15 ft) wL (6,000 N/m)(5m)
V max = = V max = =
2 2 2 2
6,000 lb 30,000 N
= = 3,000 lb = = 15,000 N
2 2
Step 2. From Fig. 2.34 this maximum shear Step 2. As shown in Fig. 2.34 this maximum
force (V max ) of 3,000 lb occurs at both the left shear force (V max ) of 15,000 N occurs at both
and right ends of the beam. the left and right ends of the beam.
Step 3. Calculate the maximum bending Step 3. Calculate the maximum bending
moment (M max ) from Eq. (2.21) as moment (M max ) from Eq. (2.21) as
wL 2 (400 1b/ft)(15 ft) 2 wL 2 (6,000 N/m)(5m) 2
M max = = M max = =
8 8 8 8
90,000 ft · lb 150,000 N · m
= = 11,250 ft · lb = = 18,750 N · m
8 8
Step 4. As shown in Fig. 2.35 this maximum Step 4. As shown in Fig. 2.35 this maximum
bending moment (M max ) of 11,250 ft · lb is lo- bending moment (M max ) of 18,750 N · mis
cated at the midpoint of the beam. located at the midpoint of the beam.

Deflection. For this loading configuration, the deflection ( ) along the beam is shown in
Fig. 2.36, and given by Eq. (2.22) for all values of the distance (x) from the left end of the
beam,
wx 3 2 3
= (L − 2 Lx + x ) (2.22)
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