Question

A 30 kN 20 kN/m 2 m C 3 m B 1. Determine the deflection at C by area moment method. 2. Compute for the midspan value of EI\delta by double integration method. 

          A
30 kN
20 kN/m
2 m
C
3 m
B
1. Determine the deflection at C by area moment method.
2. Compute for the midspan value of EI\delta by double integration method.
A 30 kN 20 kN/m 2 m C 3 m B 1. Determine the deflection at C by area moment method. 2. Compute for the midspan value of EIδby double integration method.

Added by -Ngeles G.

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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30 kN 20 kN/m 1. Determine the deflection at C by the area moment method. 2. Compute the midspan value of Ei by the double integration method.
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Transcript

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00:01 We now find the area of the shaded region.
00:03 So the shaded region is basically the area under the curve of f of x.
00:08 So we write area under the curve, if of x.
00:20 This is given by the formula integral from x equals a to x equals b, f of x dx.
00:29 Where this x equal to a is the lower bound of x or the lower bound of f of x and this x equal to b is the upper bound of f of x we can see from this shaded region the lower bound of f of x where this area starts is x equals 0 and then the upper bound of f of x where the shaded region ends is x equal to 2 so therefore here a equal to 0 and b equals 2 and we also replace the function f of x equals x squared plus 1 so let's find the area of the shaded region and this equals the definite integral from a equal to 0 so i put the lower bound as 0 upper bound is 2 and then replace f of x by x squared plus 1 so this is x squared plus 1 tx so we are going to evaluate this definite integral.
01:37 We integrate x squared using the power rule of integral.
01:41 That is this will be x raised to the power of 2 plus 1 which is 3 divided by 3.
01:46 Same number 3 plus the integral of 1dx is x.
01:51 This must be evaluated from 0 to 2...
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