Can someone please calculate delta B and fBB? Below is the answer however i dont

Question

Can someone please calculate delta B and fBB? Below is the answer however i dont know how it was calculated.

10-12. Determine the reactions at the supports, then draw the moment diagram.Assume the support at A is a pin and B and Care rollers. El is constant. Compatibility Equation: I) Use virtual work method: (-0.5556x)(87. 08x1) mM dx dx EI EI (-1.667 05556x2 (261.2 42.08x2) dx2 EI 75 (-0.4444x,0098-54x 0.8333) dx3 EI 7322 EI 7.5 (-0.444 4x3) (-1.667 0.5556 (-0.5556x) faB dx1 dur3 EI EI EI EI 45 kN 37.5 kN/m 3 m-h m- 7.5 m 45 kN 375 kN/m 37.5 kN/m 45 kN M2E 261.2 42.08 45 kN 37.5 kN/m 3m 3 m 98.54 kN 87.08 kN dx2 m2 -0.555603 15 04444 3 m 3 m 0.5556

Explanation / Answer

Calculation of delta B:

First we need to divide the span into three parts i.e., 3m, 3m and 7.5m

Now for each span we will use the formula given to calculate delta B.

For first span in order to peform integration, lower limit is 0 and higher limit is 3.

Similarly for other sections 0 to 3 and 0 to 7.5.

And now in the formula we need m and M anyways EI is constant.

From the last diagram we can identify the values of m for each span as,

Span 1 = -0.5556x1

span2 = -0.5556(3+x2) = -1.667 - 0.5556x2

span3 = -0.4444x3

Simply integrate and substitute the values,

Now for fbb only use the values of m and substitute in the formula and integrate as span wise in three parts.

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