To study the effect an earthquake has on a structure, engineers look at the way

Question

To study the effect an earthquake has on a structure, engineers look at the way a beam bends when subjected to an earth tremor. The equation D = a a cos(h/ 2L) 0 h L where L is the length of a beam and a is the maximum deflection from the vertical, has been used by engineers to calculate the deflection D at a point on the beam h ft from the ground. Suppose that a 12-ft vertical beam has a maximum deflection of 1/ 4 ft when subjected to an external force. Using differentials, estimate the difference in the deflection between the point midway on the beam and the point 1 /10 ft above it. (Round your answer to four decimal places.)

Explanation / Answer

D=a-acos(pi h/2L)

Given that a= 1/4ft for L=12ft

D1= deflection at midway on the beam (h = 6ft)

D2 = deflection at 1/10ft above midway on the beam (h = 6+0.1=6.1ft)

D1-D2 = (a- acos (pi h1/2L))-(a-acos (pi h2/2L))

= a cos (pi h1/2L)-a cos (pi h2/2L)

= 1/4 * cos (45)- 1/4 * cos (45.75)

= 1/4 * (0.7-0.697)

= 0.00075 ft

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