06-01 Chap Gere

# 06-01 Chap Gere - 6 Stresses in Beams(Advanced Topics...

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Composite Beams When solving the problems for Section 6.2, assume that the component parts of the beams are securely bonded by adhesives or connected by fasteners. Also, be sure to use the general theory for composite beams described in Sect. 6.2. Problem 6.2-1 A composite beam consisting of fiberglass faces and a core of particle board has the cross section shown in the figure. The width of the beam is 2.0 in., the thickness of the faces is 0.10 in., and the thickness of the core is 0.50 in. The beam is subjected to a bending moment of 250 lb-in. acting about the z axis. Find the maximum bending stresses s face and s core in the faces and the core, respectively, if their respective moduli of elasticity are 4 3 10 6 psi and 1.5 3 10 6 psi. Solution 6.2-1 Composite beam 6 Stresses in Beams (Advanced Topics) 375 z y C 0.50 in. 0.10 in. 0.10 in. 2.0 in. b 5 2 in. h 5 0.7 in. h c 5 0.5 in. M 5 250 lb-in. E 1 5 4 3 10 6 psi E 2 5 1.5 3 10 6 psi E 1 I 1 1 E 2 I 2 5 176,600 lb-in. 2 I 2 5 bh 3 c 12 5 0.02083 in. 4 I 1 5 b 12 ( h 3 2 h c 3 ) 5 0.03633 in. 4 From Eq. (6-6a): From Eq. (6-6b): 5 ; 531 psi s core 5 ; M ( h c / 2) E 2 E 1 I 1 1 E 2 I 2 5 ; 1980 psi s face 5 ; M ( h / 2) E 1 E 1 I 1 1 E 2 I 2 z y C 0.50 in. 0.10 in. 0.10 in. 2.0 in. 2 1

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A wood beam with cross-sectional dimensions 200 mm 3 300 mm is reinforced on its sides by steel plates 12 mm thick (see figure). The moduli of elasticity for the steel and wood are E s 5 204 GPa and E w 5 8.5 GPa, respectively. Also, the corresponding allowable stresses are s s 5 130 MPa and s w 5 8.0 MPa. Calculate the maximum permissible bending moment M max when the beam is bent about the z axis. Solution 6.2-2 Composite beam 376 CHAPTER 6 Stresses in Beams z y C 200 mm 12 mm 12 mm 300 mm b 5 200 mm t 5 12 mm h 5 300 mm E 1 5 E w 5 8.5 GPa E 2 5 E s 5 204 GPa ( s 1 ) allow 5 s w 5 8.0 MPa ( s 2 ) allow 5 s s 5 130 MPa E 1 I 1 1 E 2 I 2 5 14.84 3 10 6 N ? m 2 I 2 5 2 th 3 12 5 54 3 10 6 mm 4 I 1 5 bh 3 12 5 450 3 10 6 mm 4 M AXIMUM MOMENT BASED UPON THE WOOD (1) From Eq. (6-6a): M AXIMUM MOMENT BASED UPON THE STEEL (2) From Eq. (6-6b): S TEEL GOVERNS . M max 5 63.0 kN ? m M max 5 ( s 2 ) allow B E 1 I 1 1 E 2 I 2 ( h / 2) E 2 R 5 63.0 kN ? m M max 5 ( s 1 ) allow B E 1 I 1 1 E 2 I 2 ( h / 2) E 1 R 5 93.1 kN ? m z y C 200 mm 12 mm 12 mm 300 mm 2 1 Problem 6.2-3 A hollow box beam is constructed with webs of Douglas-fir plywood and flanges of pine as shown in the figure, which is a cross-sectional view. The plywood is 1 in. thick and 12 in. wide; the flanges are 2 in. 3 4 in. (actual size). The modulus of elasticity for the plywood is 1,600,000 psi and for the pine is 1,200,000 psi. If the allowable stresses are 2000 psi for the plywood and 1700 psi for the pine, find the allowable bending moment M max when the beam is bent about the z axis. z
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## This note was uploaded on 03/19/2008 for the course E M 316 taught by Professor Korkolis during the Spring '08 term at University of Texas.

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06-01 Chap Gere - 6 Stresses in Beams(Advanced Topics...

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