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05-05ChapGere.0013

# 05-05ChapGere.0013 - H if there is to be no tension in the...

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Problem 5.12-8 A steel bar of solid circular cross section is subjected to an axial tensile force T 5 26 kN and a bending moment M 5 3.2 kN ? m (see figure). Based upon an allowable stress in tension of 120 MPa, determine the required diameter d of the bar. (Disregard the weight of the bar itself.) Solution 5.12-8 Circular bar 362 CHAPTER 5 Stresses in Beams T 5 26 kN M 5 3.2 kN ? m s allow 5 120 MPa d 5 diameter T ENSILE STRESS or p d 3 s allow 2 4 Td 2 32 M 5 0 ( p )(120 MPa) d 3 2 4(26 kN) d 2 32(3.2 kN ? m) 5 0 s t 5 T A 1 M S 5 4 T p d 2 1 32 M p d 3 S 5 p d 3 32 A 5 p d 2 4 ( d 5 meters) (120,000,000 N / m 2 )( p ) d 3 2 (104,000 N) d 2 102,400 N ? m 5 0 S IMPLIFY THE EQUATION : (15,000 p ) d 3 2 13 d 2 12.8 5 0 S OLVE NUMERICALLY FOR THE REQUIRED DIAMETER : d 5 0.0662 m 5 66.2 mm Problem 5.12-9 A cylindrical brick chimney of height H weighs w 5 825 lb/ft of height (see figure). The inner and outer diameters are d 1 5 3 ft and d 2 5 4 ft, respectively. The wind pressure against the side of the chimney is p 5 10 lb/ft 2 of projected area. Determine the maximum height
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Unformatted text preview: H if there is to be no tension in the brickwork. Solution 5.12-9 Brick chimney p 5 wind pressure q 5 intensity of load 5 pd 2 d 2 5 outer diameter d 1 5 inner diameter W 5 total weight of chimney 5 wH C ROSS SECTION I 5 p 64 ( d 2 4 2 d 1 4 ) 5 p 64 ( d 2 2 2 d 1 2 )( d 2 2 1 d 1 2 ) A 5 p 4 ( d 2 2 2 d 1 2 ) A T BASE OF CHIMNEY N 5 W 5 wH T ENSILE STRESS ( EQUAL TO ZERO ) or S OLVE FOR H S UBSTITUTE NUMERICAL VALUES w 5 825 lb/ft d 2 5 4 ft d 1 5 3 ft p 5 10 lb/ft 2 H max 5 32.2 ft H 5 w ( d 2 2 1 d 1 2 ) 4 pd 2 2 pd 2 H 2 2 wH 5 d 2 2 1 d 1 2 8 d 2 M N 5 2 I Ad 2 s t 5 2 N A 1 Md 2 2 I 5 Ê M 5 qH ¢ H 2 ≤ 5 1 2 pd 2 H 2 I A 5 1 16 ( d 2 2 1 d 1 2 ) Ê c 5 d 2 2 M T w d 1 d 2 p H q H N V M W d 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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