Page 90 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
Brown.cls
72
U.S. Customary 16:18 STRENGTH OF MACHINES SI/Metric
Step 2. Calculate the stiffness (EI). Step 2. Calculate the stiffness (EI).
4
4
2
9
2
6
EI = (10.3 × 10 lb/in )(63 in ) EI = (71 × 10 N/m )(2,454 cm )
2
8
6.49 × 10 lb · in × 1ft 2 1m 4
= 2 × 4
144 in (100 cm)
6
6
= 4.51 × 10 lb · ft 2 = 1.74 × 10 N · m 2
Step 3. Determine the deflection ( ) from Step 3. Determine the deflection ( ) from
Eq. (2.33b). Eq. (2.33b).
Fa 2 2 Fa 2 2
= [3Lx − a − 3 x ] = [3Lx − a − 3 x ]
6 EI 6 EI
(1,000 lb)(1ft) (4,500 N)(0.3m)
= =
2
6
2
6
6 (4.51 × 10 lb · ft ) 6 (1.74 × 10 N · m )
2
2
2
2
2
2
×[(3(5)(2) − (1) − 3 (2) ) ft ] ×[(3(1.5)(0.5) − (0.3) − 3 (0.5) ) m ]
(1,000 ft · lb) (1,350 N · m)
= 2 = 7 2
7
(2.71 × 10 lb · ft ) (1.04 × 10 N · m )
2
2
×[(30 − 1 − 12) ft ] ×[(2.25 − 0.09 − 0.75)m ]

1 −4 1 2
2
= 3.69 × 10 −5 × [17 ft ] = 1.30 × 10 × [1.41 m ]
ft m
12 in 100 cm
= 0.00063 ft × = 0.000182 m ×
ft m
= 0.0075 in ↓ = 0.0182 cm ↓
Example 5. Calculate and locate the maxi- Example 5. Calculate and locate the maxi-
mum deflection ( max ) for the beam configura- mum deflection ( max ) for the beam configura-
tion of Example 4, where tion of Example 4, where
F = 1,000 lb F = 4,500 N
L = 5 ft, a = 1ft L = 1.5 m, a = 0.3 m
6
6
EI = 4.51 × 10 lb · ft 2 EI = 1.74 × 10 N · m 2
solution solution
Calculate the maximum deflection ( max ) from Calculate the maximum deflection ( max ) from
Eq. (2.34). Eq. (2.34).
Fa 2 2 Fa 2 2
max = (3L − 4 a ) max = (3L − 4 a )
24 EI 24 EI
(1,000 lb)(1ft) (4,500 N)(0.3m)
= =
2
2
6
6
24 (4.51 × 10 lb · ft ) 24 (1.74 × 10 N · m )
2
2
2
2
2
2
×[(3 (5) − 4 (1) ) ft ] ×[(3 (1.5) − 4 (0.3) ) m ]
(1,000 ft · lb) (1,350 N · m)
= = 7 2
2
8
(1.08 × 10 lb · ft ) (4.18 × 10 N · m )
2
2
×[(75 − 4) ft ] ×[(6.75 − 0.36) m ]

1 −5 1 2
2
= 9.24 × 10 −6 [71 ft ] = 3, 23 × 10 [6.39 m ]
ft m
12 in 100 cm
= 0.000656 ft × = 0.000206 m ×
ft m
= 0.0079 in ↓ = 0.0206 cm ↓