Page 136 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
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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 cantilevered beam bending moment (M) for a cantilevered beam
of length (L) with a uniform distributed load of length (L) with a uniform distributed load
(w) acting across its entire length, at a distance (w) acting across its entire length, at a distance
(x) from the left end of the beam, where (x) from the left end of the beam, where
w = 50 lb/ft w = 800 N/m
L = 5ft L = 1.5 m
x = 4ft x = 1.2 m
solution solution
Step 1. Determine the shear force (V ) from Step 1. Determine the shear force (V ) from
Eq. (2.73) as Eq. (2.73) as
V =−wx =−(50 lb/ft)(4ft) V =−wx =−(800 N/m)(1.2m)
=−200 lb =−960 N
Step 2. Determine the bending moment (M) Step 2. Determine the bending moment (M)
from Eq. (2.75). from Eq. (2.75).
wx 2 (50 lb/ft)(4ft) 2 wx 2 (800 N/m)(1.2m) 2
M =− =− M =− =−
2 2 2 2
800 ft · lb 1,152 N · m
=− =−
2 2
=−400 ft · lb =−576 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 = 50 lb/ft w = 800 N/m
L = 5ft L = 1.5 m
solution solution
Step 1. Calculate the maximum shear force Step 1. Calculate the maximum shear force
(V max ) from Eq. (2.74) as (V max ) from Eq. (2.74) as
V max = wL = (50 lb/ft)(5ft) V max = wL = (800 N/m)(1.5m)
= 250 lb = 1,200 N
Step 2. As shown in Fig. 2.108, this maximum Step 2. As shown in Fig. 2.108, this maximum
shear force (V max ) of 250 lb occurs at the right shear force (V max ) of 1,200 N occurs at the right
end of the beam. end of the beam.
Step 3. Calculate the maximum bending Step 3. Calculate the maximum bending
moment (M max ) from Eq. (2.76) as moment (M max ) from Eq. (2.76) as
wL 2 (50 lb/ft)(5ft) 2 wL 2 (800 N/m)(1.5m) 2
M max = = M max = =
2 2 2 2
1,250 ft · lb 1,800 N · m
= = 625 ft · lb = = 900 N · m
2 2