1. Home Work #8

2. 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?

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

4. 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.

5. 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= m
P=67.5 N

6. 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).

7. 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

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

9. 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.

10. HW 8-Problem #4