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678_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 678_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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672 CHAPTER 8 Applications of Plane Stress Problem *8.4-10 A cantilever beam of T-section is loaded by an inclined force of magnitude 6.5 kN (see figure). The line of action of the force is inclined at an angle of 60° to the horizontal and intersects the top of the beam at the end cross section. The beam is 2.5 m long and the cross section has the dimensions shown. Determine the principal stresses s 1 and s 2 and the maximum shear stress t max at points A and B in the web of the beam near the support. Q 5.219 in. 3 t xy 736.289 psi t max 1777 psi ; t max A a s x s y 2 b 2 + t xy 2 s 2 3393 psi ; s 2 s x + s y 2 A a s x s y 2 b 2 + t xy 2 s 1 159.8 psi ; s 1 s x + s y 2 + A a s x s y 2 b 2 + t xy 2 t xy V Q I t w Q b a h h 1 2 b a h + h 1 4 b ( C ) N EUTRAL AXIS ( POINT C ) s x 0 s y 0 Q 8.502 in 3 t xy 1.2 10 3 psi Pure shear: s 2 s 1 t max t xy t max 1200 psi
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