671_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

671_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 8.4 Maximum Stresses in Beams 665 Problem 8.4-2 Solve the preceding problem for the following data: P ± 130 kN, b ± 80 mm, h ± 260 mm, c ± 0.6 m, and d ± 220 mm. Solution 8.4-2 P ± 130 kN c ± 0.6 m b ± 80 mm d ± 220 mm h ± 260 mm v ± 0.3 S TRESS AT POINT A I ± 1.172 ² 10 8 mm 4 M ±³ Pc M 7.8 ² 10 4 Nm V ± PV ± 1.3 ² 10 5 N y A ± 90 mm s x ± 59.911 MPa Q ± 3.52 ² 10 5 mm 3 t ± 4.882 MPa t xy ± t s x ± 59.911 MPa s y ± 0 t xy ± 4.882 MPa P RINCIPAL STRESSES u p ± 4.628 deg u p ± 1 2 a tan a 2 t xy s x ³ s y b tan(2 u p ) ± 2 t xy s x ³ s y ± 2 t xy s x ³ s y ± 0.163 t ± VQ Ib Q ± bd a h 2 ³ d 2 b s x My A I y A h 2 + d # I ± bh 3 12 For u 1 ± u p u 1 ± 4.628 deg s x 1 ± 60.306 MPa For u 2 ± 90 deg ´ u p u 2 ± 94.628 deg s x 2 0.395 MPa Therefore s 1 ± s x 1 u p 1 ± u 1 s 2 ± s x 2 u p 2 ± u 2 M AXIMUM SHEAR STRESSES u s 1 ± u p 1 ³ 45 deg u s 2 ± u s 1 ´ 90 deg s avg ± 30.0 deg ; s avg ± s x + s y 2 u s 2 ± 49.6 deg ; u s 1 40.4 deg ; t max ± 30.4 MPa ; t max ± A a s x ³ s y 2 b 2 + t xy 2 u p 2 ± 94.6 deg ; s 2 0.395 MPa ; u p 1 ± 4.63 deg ; s 1 ± 60.3 MPa ; + t xy sin (2 u 2 ) s x 2 ± s x + s y 2 + s x ³ s y 2 cos (2 u 2 ) + t xy sin (2 u 1 ) s x 1 ± s x + s y 2 + s x ³ s y 2 cos (2 u 1 ) Problem 8.4-3 A simple beam of rectangular cross section
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