Home Work #8.

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Presentation transcript:

Home Work #8

HW 8-Problem #1 The beam is subjected to a uniform load w. Determine the placement a of the supports so that the shear stress in the beam is as small as possible. What is this stress?

HW 8-Problem #1 w For 0<x<a V x For a<x<(L-a) For (L-a)<x<L

HW 8-Problem #2 The fence board weaves between the three smooth fixed posts. If the posts remain along the same line, determine the maximum bending stress in the board. The board has a width of 150mm and a thickness of 12mm. E=12Gpa. Assume the displacement of each end of the board relative to its center is 75mm.

HW 8-Problem #2 For 0<x<L/2 Y=0 at x=0; C2=0 x=L, dy/dx=0; C1=-PL2/16 At x=1.2m; y= -0.075 m P=67.5 N

HW 8-Problem #3 Determine the equation of the deflection of the beam and specify the slope at B and deflection at C. EI is constant. (please ignore x1, x2 and x3).

HW 8-Problem #3 For 0<x<a For a<x<2a For 0<x<a For x=0 y=0; C2=0 For x=0 dy/dx=0; C1=0

HW 8-Problem #3 For a<x<2a For x=a At point B x=2a At point C x=a

HW 8-Problem #4 The beam is supported by a pin at A, a spring having a stiffness k at B, and a roller at C. Use method of superposition to determine the force the spring exerts on the beam. EI is constant.

HW 8-Problem #4