Page 101 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
16:18
Brown.cls
Brown˙C02
U.S. Customary BEAMS SI/Metric 83
solution solution
Step 1. As the distance (x) is less than the Step 1. As the distance (x) is less than the
length (L), the shear force (V ) is determined length (L), the shear force (V ) is determined
from Eq. (2.41a)as from Eq. (2.41a)as
w 2 2 w 2 2
V = (L − a ) − wx V = (L − a ) − wx
2L 2L
(113 lb/ft) 2 2 (1,540 N/m) 2 2
= [(3ft) − (1ft) ] = [(1m) − (0.3m) ]
2 (3ft) 2 (1m)
− (113 lb/ft)(2ft) − (1,540 N/m)(0.6m)
(113 lb/ft) 2 2 (1,540 N/m) 2 2
= [9 ft − 1ft ] = [1 m − 0.09 m ]
(6ft) (2m)
− (226 lb) − (924 N)
2
2
2
2
= (18.83 lb/ft )[8 ft ] = (770 N/m )[0.91 m ]
− (226 lb) − (924 N)
= (151 lb) − (226 lb) = (701 N) − (924 N)
=−75 lb =−223 N
Step 2. As the distance (x) is less than the Step 2. As the distance (x) is less than the
length (L), the bending moment (M) is deter- length (L), the bending moment (M) is deter-
mined from Eq. (2.44a)as mined from Eq. (2.44a)as
wx 2 2 wx 2 2
M = (L − a − Lx) M = (L − a − Lx)
2L 2L
(113 1b/ft)(2ft) (1,540 N/m)(0.6m)
= =
2 (3ft) 2 (1m)
2
2
2
2
× [(3ft) − (1ft) − (3ft)(1ft)] ×[(1m) − (0.3m) − (1m)(0.3m)]
(226 1b) (924 N)
2
2
2
2
2
2
= [9 ft − 1ft − 3ft ] = [1 m − 0.09 m − 0.3m ]
(6ft) (2m)
2
2
= (37.67 lb/ft) [5 ft ] = (462 N/m)[0.61 m ]
= 188 ft · lb = 282 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
Example 2, where Example 2, where
w = 113 lb/ft w = 1,540 N/m
L = 3 ft, a = 1ft L = 1m, a = 0.3 m
solution solution
Step 1. Calculate the maximum shear force Step 1. Calculate the maximum shear force
(V max ) from Eq. (2.43) as (V max ) from Eq. (2.43) as
w 2 2 w 2 2
V max = (L + a ) V max = (L + a )
2L 2L
(113 lb/ft) 2 2 (1,540 N/m) 2 2
V max = [(3ft) + (1ft) ] V max = [(1m) + (0.3m) ]
2 (3ft) 2 (1m)
(113 lb/ft) 2 2 (1,540 N/m) 2 2
= [9 ft + 1ft ] = [1 m + 0.09 m ]
(6ft) (2m)

18.83 lb 2 770 N 2
= 2 [10 ft ] = 188 lb = 2 [1.09 m ] = 839 N
ft m