512_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

512_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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506 CHAPTER 6 Stresses in Beams (Advanced Topics) Problem 6.2-11 A simply supported wooden I-beam with a 12 ft span supports a distributed load of intensity q ± 90 lb/ft over its length (see figure part a). The beam is constructed with a web of Douglas-fir plywood and flanges of pine glued to the web as shown in the figure part b. The plywood is 3/8 in. thick; the flanges are 2 in. ² 2 in. (actual size). The modulus of elasticity for the plywood is 1,600,000 psi and for the pine is 1,200,000 psi. (a) Calculate the maximum bending stresses in the pine flanges and in the plywood web. (b) What is q max if allowable stresses are 1600 psi in the flanges and 1200 psi in the web? (10 GPa)( h 1 ³ 75)(100)(150)(10 ³ 9 ) ´ (210 GPa)( h 1 ³ 154)(100)(8)(10 ³ 9 ) ± 0 Solve for h 1 : h 1 ± 116.74 mm h 2 ± h ´ t ³ h 1 ± 41.26 mm M OMENTS OF INERTIA ( FROM PARALLEL - AXIS THEOREM ) E 1 I 1 + E 2 I 2 ± 776,750 N # m 2 I 2 ± bt 2 12 + bt ( h 2 ³ t /2) 2 ± 1.115 * 10 6 mm 4 I 1 ± bh 3 12 + bh ( h 1 ³ h /2) 2 ± 54.26 * 10 6 mm 4 M AXIMUM STRESSES (E QS . 6-6a AND b) ± 37.6MPa (Tension)
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Unformatted text preview: ; s s s 2 Mh 2 E 2 E 1 I 1 + E 2 I 2 5.1MPa (Compression) ; s w s 1 Mh 1 E 1 E 1 I 1 + E 2 I 2 Solution 6.2-11 (a) M AXIMUM BENDING STRESSES Plywood (1): h 1 7 in. Pine (2): b 2 in. h 2 2 in. E pine 1.2 * 10 6 psi a 1 2 in. I 1 t h 3 1 12 I 1 10.72 in. 4 E plywood 1.6 * 10 6 psi t 3 8 in. M max qL 2 8 M max 1620 lb # ft q 90 lb/f L 12ft E plywood I 1 E pine I 2 96.287 10 6 lbin. 2 s plywood 1131 psi ; s plywood M max a h 1 2 b E plywood E plywood I 1 + E pine I 2 I 2 65.95 in. 4 ; + ( b t )( h 2 a ) a h 1 2 h 2 a 2 b 2 d I 2 2 c ba 3 12 + ba a h 1 + a 2 b 2 + ( b t )( h 2 a ) 3 12 C 2 in. 2 in. 2 in. 2 in. 2 in. pine flange in. plywood (Douglas fir) 8 in. y z 3 8 in. 1 2 (b) 12 ft q A B (a) 06Ch06.qxd 9/24/08 5:32 AM Page 506...
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