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515_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 515_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.3 Transformed-Section Method 509 300 mm 75 mm 75 mm 100 mm t t z y C Problem 6.3-2 A simple beam of span length 3.2 m carries a uniform load of intensity 48 kN/m. The cross section of the beam is a hollow box with wood flanges and steel side plates, as shown in the figure. The wood flanges are 75 mm by 100 mm in cross section, and the steel plates are 300 mm deep. What is the required thickness t of the steel plates if the allowable stresses are 120 MPa for the steel and 6.5 MPa for the wood? (Assume that the moduli of elasticity for the steel and wood are 210 GPa and 10 GPa, respectively, and disregard the weight of the beam.) Solution 6.3-1 (a) F IND M max (1) Wood beam b ± 7.5 in. h 1 ± 11.5 in. s allow_w ± 1100 psi (2) Steel plates b ± 7.5 in. h 2 ± 12 in. t ± 0.25 in. s allow_s ± 15000 psi T RANSFORMED SECTION ( WOOD ) n ± 20 W IDTH OF STEEL PLATES M AXIMUM MOMENT BASED UPON THE WOOD (1) M AXIMUM MOMENT BASED UPON THE STEEL (2)
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Unformatted text preview: M 2 ± s allow_s I h 2 n 2 T M 2 ± 442 k # in. M 1 ± s allow_w I T h 1 2 M 1 ± 677 k # in. I T ± 3540 in. 4 I T ± bh 3 1 12 + 2 c t 3 b T 12 + t b T a h 2 ² t 2 b 2 d b T ± nb b T ± 150 in. S TELL GOVERNS (b) C OMPARE MOMENT CAPACITIES (1) Wood beam b ± 3.5 in. h 1 ± 11.25 in. (2) Steel plates h 2 ± 11 in. t ± 0.25 in. W IDTH OF STEEL PLATES M AXIMUM MOMENT BASED UPON THE WOOD (1) M AXIMUM MOMENT BASED UPON THE STEEL (2) S TELL GOVERNS . T HE MOMENT CAPACITY OF THE BEAM IN (a) IS 2.3 TIMES MORE THAN THE BEAM IN (b) M max ± 189 k-in. ; M max ± min( M 1 , M 2 ) M 2 ± s allow_s I T h 2 n 2 M 2 ± 189 k # in. M 1 ± s allow_w I T h 1 2 M 1 ± 271 k # in. I T ± 2 bh 3 1 12 + b T h 3 2 12 I T ± 1385 in. 4 b T ± nt b T ± 5 in. M max ± 422 k-in. ; M max ± min( M 1 , M 2 ) 06Ch06.qxd 9/24/08 5:32 AM Page 509...
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