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Homework#9-Solutions

# Homework#9-Solutions - 05Ch05.qxd 444 2:29 PM Page 444...

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444 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.8-4 Shear stresses in a cantilever beam Eq. (5-39): t 50 * 10 6 (10,000 y 1 2 ) ( y 1 mm; t MPa) t 8,000 2(80 * 10 6 ) c (200) 2 4 y 1 2 d ( t N/mm 2 MPa) h 200 mm ( y 1 mm) I bh 3 12 80 * 10 6 mm 4 V P 8.0 kN 8,000 N t V 2 I a h 2 4 y 1 2 b Distance from the y 1 top surface (mm) (mm) 0 100 0 0 25 75 0.219 219 50 50 0.375 375 75 25 0.469 469 100 (N.A.) 0 0.500 500 G RAPH OF SHEAR STRESS t (kPa) (MPa) t t Solution 5.8-3 Maximum load M max q 5.833 1b ft q g A weight of beam per unit distance g 35 lb ft 3 A b # h h 6 in. t allow 200 psi L 8 ft b 4 in. ; M max 25.4 k-ft M max 2 AL 3 t allow qL 2 2 M 2 AL 3 t max qL 2 2 t max 3 V 2 A 3 2 A a M L + qL 2 b V M L + qL 2 Problem 5.8-4 A cantilever beam of length supports a load (see figure). The beam is made of wood with cross-sectional dimensions . Calculate the shear stresses due to the load at points located , , and from the top surface of the beam. from these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam. 100 mm 75 mm 25 mm P 120 mm * 200 mm P 8.0 kN L 2 m 200 mm 120 mm L = 2 m P = 8.0 kN 05Ch05.qxd 9/25/08 2:29 PM Page 444

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SECTION 5.8 Shear Stresses in Rectangular Beams 449 Solution 5.8-10 Simply supported wood beam L 1.2 m q g bh 181.44 N/m g 5.4 kN/m 3 S bh 2 6 1344 * 10 3 mm 3 A bh 33,600 mm 2 b 140 mm h 240 mm (a) A LLOWABLE BASED UPON BENDING STRESS Equate values of and solve for : or P 38.0 kN ; 0.3 P + 32.66 11,424 P 37,970 N P M max 11,424 N # m M max S s allow (1344 * 10 3 mm 3 )(8.5 MPa) ( P newtons; M N # m) 0.3 P + 32.66 N # m + (181.44 N/m)(1.2 m) 2 8 M max PL 4 + qL 2 8 P (1.2 m) 4 s allow 8.5 MPa s M max S P From Appendix F: Select in. beam (nominal dimensions) (b) R EPEAT ( A ) CONSIDERING THE WEIGHT OF THE BEAM R B 7.83 * 10 3 1b R B 7.725 * 10 3 1b + q beam L 2 q beam 20.964 1b ft g 35 1b ft 3 q beam g A A 86.25 in. 2 S 165.3 in. 3 ; 8 * 12 s max M S S req M max s allow S req 120.6 in. 3 beam is still satisfactory for shear. beam is still satisfactory for moment. ; Use 8 * 12 in. beam 8 * 12 S req M max s allow S req 122.3 in. 3 < S M max 2.293 * 10 4 1b-ft M max R B d qd 2 2 q total q + q beam q total 145.964 1b ft 8 * 12 A req 73.405 in. 2 < A V max R B A req 3 V max 2 t allow Problem 5.8-10 A simply supported wood beam of rectangular cross section and span length carries a concentrated load at midspan in addition to its own weight (see figure). The cross section has width and height . The weight density of the wood is .
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