Page 96 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
78
U.S. Customary 16:18 STRENGTH OF MACHINES SI/Metric
Step 2. As the distance (x) is less than the Step 2. As the distance (x) is less than the
length (L), the deflection ( ) is determined length (L), the deflection ( ) is determined
from Eq. (2.38a). from Eq. (2.38a).
Fax 2 2 Fax 2 2
= (L − x ) ↑ = (L − x ) ↑
6 EIL 6 EIL
(450 lb)(1ft)(2ft) (2,000 N)(0.3m)(0.6m)
= =
6
2
2
6
6 (2.5 × 10 lb · ft )(3ft) 6 (1.02 × 10 N · m )(1m)
2
2
2
2
×[(3ft) − (2ft) ] × [(1m) − (0.6m) ]
2
2
(900 lb · ft ) (360 N · m )
= = 6 3
3
7
(4.5 × 10 lb · ft ) (6.12 × 10 N · m )
2
2
2
2
×[(9ft ) − (4ft )] ×[(1m ) − (0.36 m )]

1 −5 1 2
2
= 2.0 × 10 −5 × [5 ft ] = 5.88 × 10 × [0.64 m ]
ft m
12 in 100 cm
= 0.0001 ft × = 0.000038 m × m
ft
= 0.0012 in ↑ = 0.0038 cm ↑
Example 5. Calculate the maximum down- Example 5. Calculate the maximum down-
ward deflection ( max ) for the beam configu- ward deflection ( max ) for the beam configu-
ration in Example 4, where ration in Example 4, where
F = 450 lb F = 2,000 N
L = 3 ft, a = 1ft L = 1m, a = 0.3 m
6
6
EI = 2.5 × 10 lb · ft 2 EI = 1.02 × 10 N · m 2
solution solution
The maximum downward deflection occurs at The maximum downward deflection occurs at
the free end where the force (F) acts, and is the free end where the force (F) acts, and is
determined from Eq. (2.40). determined from Eq. (2.40).
Fa 2 Fa 2
max = (L + a) max = (L + a)
3 EI 3 EI
(450 lb)(1ft) 2 (2,000 N)(0.3m) 2
= 2 (3ft + 1ft) = 6 2 (1m + 0.3m)
6
3 (2.5 × 10 lb · ft ) 3 (1.02 × 10 N · m )
450 lb · ft 2 180 N · m 2
= (4ft) = 6 2 (1.3m)
6
7.5 × 10 lb · ft 2 3.06 × 10 N · m
= (6.0 × 10 −5 )(4ft) = (5.88 × 10 −5 )(1.3m)
12 in 100 cm
= 0.00024 ft × = 0.000076 m × m
ft
= 0.0029 in ↓ = 0.0076 cm ↓
Example 6. Calculate and locate the maxi- Example 6. Calculate and locate the maxi-
mum upward deflection ( max ) for the beam mum upward deflection ( max ) for the beam
configuration of Example 4, where configuration of Example 4, where
F = 450 lb F = 2,000 N
L = 3 ft, a = 1ft L = 1m, a = 0.3 m
6
6
EI = 2.5 × 10 lb · ft 2 EI = 1.02 × 10 N · m 2