Page 127 - Marks Calculation for Machine Design

P1: Sanjay
16:18
January 4, 2005
Brown.cls
Brown˙C02
U.S. Customary BEAMS SI/Metric 109
Example 5. Calculate the maximum deflec- Example 5. Calculate the maximum deflec-
tion ( max ) and its location for the beam con- tion ( max ) and its location for the beam con-
figuration in Example 4, where figuration in Example 4, where
F = 150 lb F = 700 N
L = 8ft L = 2.5 m
a = 3 ft, b = 5ft a = 1m, b = 1.5 m
5
6
EI = 1.61 × 10 lb · ft 2 EI = 6.64 × 10 N · m 2
solution solution
Step 1. Calculate the maximum deflection at Step 1. Calculate the maximum deflection at
the free end from Eq. (2.67). the free end from Eq. (2.67).
Fb 2 Fb 2
max = (3L − b) max = (3L − b)
6 (EI) 6 (EI)
(150 lb)(5ft) 2 (700 N)(1.5m) 2
= 2 = 5 2
6
6 (1.61 × 10 lb · ft ) 6 (6.64 × 10 N · m )
×[3 (8ft) − 5ft)] ×[3 (2.5m) − 1.5m)]
3
3
3.75 × 10 lb · ft 2 1.575 × 10 N · m 2
= = 6 2
6
9.66 × 10 lb · ft 2 3.98 × 10 N · m
×[(24 − 5) ft] ×[(7.5 − 1.5) m]
= (3.88 × 10 −4 ) × (19 ft) = (3.96 × 10 −4 ) × (6m)
12 in 100 cm
= 0.00737 ft × = 0.00237 m ×
ft m
= 0.088 in ↓ = 0.237 cm ↓
Example 6. Calculate the deflection ( a ) Example 6. Calculate the deflection ( a )
where the force (F) acts, where where the force (F) acts, where
F = 150 lb F = 700 N
L = 8ft L = 2.5 m
a = 3 ft, b = 5ft a = 1m, b = 1.5 m
6
5
EI = 1.61 × 10 lb · ft 2 EI = 6.64 × 10 N · m 2
solution solution
Step 1. Calculate the deflection ( a ) where Step 1. Calculate the deflection ( a ) where
the force (F) acts from Eq. (2.68). the force (F) acts from Eq. (2.68).
Fb 3 Fb 3
a = a =
3 (EI) 3 (EI)
(150 lb)(5ft) 3 (700 N)(1.5m) 3
= =
2
2
5
6
3 (1.61 × 10 lb · ft ) 3 (6.64 × 10 N · m )
3
4
1.875 × 10 lb · ft 3 2.363 × 10 N · m 3
= = 6 2
6
4.83 × 10 lb · ft 2 1.99 × 10 N · m
12 in 100 cm
= 0.0039 ft × = 0.00119 m × m
ft
= 0.047 in ↓ = 0.119 cm ↓