05-01ChapGere.0017

05-01ChapGere.0017 - L 3 5 5 ft 5 60 in. P 5 625 lb q 5 80...

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Solution 5.5-20 Accelerating frame SECTION 5.5 Normal Stresses in Beamss 301 L 5 length of vertical arm t 5 thickness of vertical arm r 5 mass density a 0 5 acceleration Let b 5 width of arm perpendicular to the plane of the figure Let q 5 inertia force per unit distance along vertical arm V ERTICAL ARM S 5 bt 2 6 Ê s max 5 M max S 5 3 r L 2 a 0 t q 5 r bta 0 Ê M max 5 qL 2 2 5 r bta 0 L 2 2 T YPICAL UNITS FOR USE IN THE PRECEDING EQUATION SI UNITS : r 5 kg/m 3 5 N ? s 2 /m 4 L 5 meters (m) a 0 5 m/s 2 t 5 meters (m) s max 5 N/m 2 (pascals) USCS UNITS : r 5 slug/ft 3 5 lb-s 2 /ft 4 L 5 ft a 0 5 ft/s 2 t 5 ft s max 5 lb/ft 2 (Divide by 144 to obtain psi) q L t Problem 5.5-21 A beam of T-section is supported and loaded as shown in the figure. The cross section has width b 5 2 1/2 in., height h 5 3 in., and thickness t 5 1/2 in. Determine the maximum tensile and compressive stresses in the beam. Solution 5.5-21 Beam of T-section q = 80 lb/ft P = 625 lb h = 3 in. b = 2 in . 1 2 L 1 = 4 ft L 3 = 5 ft L 2 = 8 ft t = 1 2 in . t = 1 2 in . L 1 5 4 ft 5 48 in. L 2 5 8 ft 5 96 in.
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Unformatted text preview: L 3 5 5 ft 5 60 in. P 5 625 lb q 5 80 lb/ft 5 6.6667 lb/in. P ROPERTIES OF THE CROSS SECTION b 5 2.5 in. h 5 3.0 in. t 5 0.5 in. A 5 bt 1 ( h 2 t ) t 5 2.50 in. 2 c 1 5 2.0 in. c 2 5 1.0 in. R EACTIONS R A 5 187.5 lb (upward) R B 5 837.5 lb (upward) I C 5 25 12 in. 4 5 2.0833 in. 4 B ENDING-MOMENT DIAGRAM A T CROSS SECTION OF MAXIMUM POSITIVE BENDING MOMENT A T CROSS SECTION OF MAXIMUM NEGATIVE BENDING MOMENT M AXIMUM STRESSES s t 5 11,520 psi s c 5 8,640 psi s t 5 M 2 c 1 I C 5 11,520 psi s c 5 M 2 c 2 I C 5 5,760 psi s t 5 M 1 c 2 I C 5 4,320 psi s c 5 M 1 c 1 I C 5 8,640 psi q P L 1 L 3 L 2 R A R B A B C h b C t t c 1 c 2 M 1 5 R A L 1 5 9,000 lb in. M 2 5 ] qL 3 2 5 ] 12,000 lb in. ] 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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