404_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 404_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 398 4:59 AM Page 398 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.5-9 NUMERICAL DATA 9k FC Mmax I BC MAX. BENDING STRESS AT B 16 ft F C (BC) 1 (8) (22)3 12 * [22 Mmax 144 k-ft 1 (8 12 smax 0.625) 3 2 (0.875)] I smax 3 Mmax (12) a 22 b 2 I ; 9.53 ksi 4 1.995 * 10 in. Problem 5.5-10 A railroad tie (or sleeper) is subjected to two rail loads, each of magnitude P 175 kN, acting as shown in the figure. The reaction q of the ballast is assumed to be uniformly distributed over the length of the tie, which has cross-sectional dimensions b 300 mm and h 250 mm. Calculate the maximum bending stress smax in the tie due to the loads P, assuming the distance L 1500 mm and the overhang length a 500 mm. P a P b a L h q Solution 5.5-10 Railroad tie (or sleeper) P 175 kN L 1500 mm q DATA 2P L + 2a b 300 mm a S h 250 mm M1 500 mm bh2 6 3.125 * 10 Substitute numerical values: 3 m3 Mmax 17,500 N # m 21,875 N # m M2 21,875 N # m MAXIMUM BENDING STRESS BENDING-MOMENT DIAGRAM smax Mmax 5 21,875 N # m 3.125 * 10 3 m3 7.0 MPa (Tension on top; compression on bottom) M1 qa2 2 M2 2 qL a + ab 22 Pa2 L + 2a PL 2 2 L P a + ab L + 2a 2 P (2a 4 L) PL 2 ; ...
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