Question

A diving board is simply supported with an overhang portion from C to B. A diverstanding at the free end B has weight W = 205 lb. Assume the diving board has constant properties El with length L-8 f and E-10,000 ksi. Use these bending moment equations to answer the questions below: M.(x) = -2Wx (0 SX S1/3) M2(x) = Wx-WL, (L/3 SXSL) W ΕΙ h=2.5 int B le b-17 in- 1/3 (a) Use the method of integration to determine the slope vx) and deflection (x) equations for the entire beam. Clearly state and box the conditions used to solve for the constants of integration. (b) If the maximum allowable deflection of the beam at free end B is 8 -0.250 in., then what is the largest weight W.. [/b] of a diver that the overhang portion of the diving board can sustain? Use the moment-area method to address this problem.

Answer 1

W vu 17" اث 43 K L 71 W= 205 lb L= 8 ft E = 10,000 hoi for ozu24 Mr = - 2 Wn - wn 9 Eiday dne EI dn -PW22 ta EI Y = - Wao t can the at n=0 y=0 >> (=0 = 43 y=0 0 = - (43) + (1x40 → WL2 no

AO for ocn22% olope = dy : 1/2 (-wn2 + WL2 Wt) da EI omd y= 흩 who Her) for 2 <n<L My = Wn- WL S EI dry Wn-WL daz - EI dy an + W22 + Wn2 2 WLn ty from o at n=43 EI dy = wil In + WL2 27 n = 4 - - 2 WL2 27

from en n=4 at - 2 WL2 27 W. L2 WL 2 + G = 11 sy WL2 10 EI y W n3 2 WL na 발 + 11 win ऽ4 x 34 th at n=1/3 Y=0 0 = w L? 6 27 WL L2 2 g + 1 WLOL th sy Wee. It > 4 = (WWL)

for 4320<2 solope, dy da EI Win + 11 WL² su y = // il Wn3 6 -WLn2 + 11 went sy -1_W suy 2 6 Imax о N=L. y = 읊 WL3 6 WL 22 + 11 WL²L EI Max ऽप - 4 We Y max = -4 WL3 LE 8X12" 27. EL E = 104 keb/int 0.25 = +4 Wx18x1272 27 104 XI I- hxb 2 2.50 x 17 12 22.1354 in

0.25 = 4 WX (8X12) 27 104 x 22.134 W= 0.42 2 2 kib W= 422.2 lb } maximum allowable load for Ymax= 0.25 in.