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489_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 489_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/25/08 2:29 PM Page 483 483 SECTION 5.12 Beams with Axial Loads Problem 5.12-10 A flying buttress transmits a load P 25 kN, acting at an angle of 60° to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h 5.0 m and rectangular cross section of thickness t 1.5 m and width b 1.0 m (perpendicular to the plane of the figure). The stone used in the construction weighs y 26 kN/m3. What is the required weight W of the pedestal and statue above the vertical buttress (that is, above section A) to avoid any tensile stresses in the vertical buttress? Flying buttress P W 60° A A t — 2 h t B Solution 5.12-10 h t B Flying buttress FREE-BODY DIAGRAM OF VERTICAL BUTTRESS CROSS SECTION A bt S 12 bt 6 1.5 m2 (1.0 m)(1.5 m) 1 (1.0 m)(1.5 m)2 6 0.375 m3 AT THE BASE N W + WB + P sin 60° W + 195 kN + (25 kN) sin 60° W + 216.651 kN M (25 kN) (cos 60°) (5.0 m) (Pcos 60°) h 62.5 kN # m TENSILE STRESS (EQUAL TO ZERO) P 25 kN h 5.0 m t 1.5 m N M + A S st b b 1.0 m 2 width of buttress perpendicular to the figure g WB 26 kN/m weight of vertical buttress 195 kN 1.5 m or 3 bthg 62.5 kN # m W + 216.651 kN W W 33.3 kN + 0.375 m3 216.651 kN + 250 kN ; 0 0 ...
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