Page 121 - Marks Calculation for Machine Design

P1: Sanjay
16:18
January 4, 2005
Brown.cls
Brown˙C02
U.S. Customary BEAMS SI/Metric 103
solution solution
Step 1. Calculate the stiffness (EI). Step 1. Calculate the stiffness (EI).
9
4
2
4
6
2
EI = (1.6 × 10 lb/in )(145 in ) EI = (11 × 10 N/m )(6,035 cm )
1ft 2 1m 4
8 2
= 2.32 × 10 lb · in × 2 × 4
144 in (100 cm)
6
5
= 1.61 × 10 lb · ft 2 = 6.64 × 10 N · m 2
Step 2. Determine the deflection ( ) from Step 2. Determine the deflection ( ) from
Eq. (2.61). Eq. (2.61).
F 3 2 3 F 3 2 3
= (2L − 3L x + x ) = (2L − 3L x + x )
6 (EI) 6 (EI)
(150 lb) (700 N) 3
= = [2(2.5m)
2
6
2
5
6 (1.61 × 10 lb · ft ) 6 (6.64 × 10 N · m )
2
3
2
3
3
×[2 (8ft) − 3 (8ft) (3ft) + (3ft) ] − 3(2.5m) (1m) + (1m) ]
(150 lb) (700 N)
= =
6
2
2
6
(9.66 × 10 lb · ft ) (3.98 × 10 N · m )
3
3
×[(1024 − 576 + 27) ft ] ×[(31.25 − 18.75 + 1) m ]
1 1
3
3
= 1.553 × 10 −5 × (475 ft ) = 1.76 × 10 −4 2 × (13.5m )
ft 2 m
12 in 100 cm
= 0.0074 ft × = 0.09 in ↓ = 0.0024 m × = 0.24 cm ↓
ft m
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
6
5
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. (2.62). the free end from Eq. (2.62).
FL 3 FL 3
max = max =
3 (EI) 3 (EI)
(150 lb)(8ft) 3 (700 N)(2.5m) 3
= =
2
2
5
6
3 (1.61 × 10 lb · ft ) 3 (6.64 × 10 N · m )
4
4
7.68 × 10 lb · ft 3 1.09 × 10 N · m 3
= = 6 2
6
4.83 × 10 lb · ft 2 1.99 × 10 N · m
12 in 100 cm
= 0.0159 ft × = 0.19 in ↓ = 0.0055 m × = 0.55 cm ↓
ft m