Page 84 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
Brown˙C02
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66
U.S. Customary 16:18 STRENGTH OF MACHINES SI/Metric
Example 4. Calculate the deflection ( ) at Example 4. Calculate the deflection ( ) at
a distance (x) equal to (L/2) for a simply- a distance (x) equal to (L/2) for a simply-
supported beam of length (L) with a triangu- supported beam of length (L) with a triangu-
lar load (w) from left to right across the beam, lar load (w) from left to right across the beam,
where where
w = 750 lb/ft w = 10,000 N/m
L = 6ft L = 1.8 m
6
9
2
2
E = 30 × 10 lb/in (steel) E = 207 × 10 N/m (steel)
I = 28 in 4 I = 1,098 cm 4
solution solution
Step 1. Determine the distance (x). Step 1. Determine the distance (x).
L 6ft L 1.8m
x = = = 3ft x = = = 0.9m
2 2 2 2
Step 2. Calculate the stiffness (EI). Step 2. Calculate the stiffness (EI).
6
9
2
4
4
2
EI = (30 × 10 lb/in )(28 in ) EI = (207 × 10 N/m )(1,098 cm )
8
2
8.40 × 10 lb · in × 1ft 2 1m 4
= ×
144 in 2 (100 cm) 4
6
6
= 5.83 × 10 lb · ft 2 = 2.27 × 10 N · m 2
Step 3. Determine the deflection ( ) from Step 3. Determine the deflection ( ) from
Eq. (2.28). Eq. (2.28).
wx 4 2 2 4 wx 4 2 2 4
= (7 L − 10 L x + 3 x ) = (7 L − 10 L x + 3 x )
360 (EI) L 360 (EI) L
(750 lb/ft)(3ft) (10,000 N/m)(0.9m)
= 2 =
6
6
2
360 (5.83 × 10 lb · ft )(6ft) 360 (2.27 × 10 N · m )(1.8m)
2
4
4
2
2
4
× [7(6ft) − 10(6ft) (3ft) + 3(3ft) ] ×[7(1.8m) − 10(1.8m) (0.9m) 2
4
+3(0.9m) ]
(2,250 lb) (9,000 N)
= =
3
9
10
3
(1.26 × 10 lb · ft ) (1.47 × 10 N · m )
4
4
×[(9,072) − (3,240) + (243) ft ] ×[(73.48) − (26.24) + (1.97) m ]
1 1
4
4
= 1.79 × 10 −7 × [6,075 ft ] = 6.11 × 10 −6 × [49.21 m ]
ft 3 m 3
12 in 100 cm
= 0.001085 ft × = 0.0130 in ↓ = 0.000301 m × = 0.0301 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
w = 750 lb/ft w = 10,000 N/m
L = 6ft L = 1.8 m
6
6
EI = 5.83 × 10 lb · ft 2 EI = 2.27 × 10 N · m 2