Strength of Materials

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63 (b) cannot be determined from the curves (a) and (b) curve (c') must be employed. For the arbitrary constant A\ chosen in Fig. 63 (b) curve (c f ) shows a value of zero at the left end and a negative value X"X' at the right end. This shows that the negative area exceeded the positive area by the amount X"X' '. Suppose that the values at each end should have been zero, the curve then should end at X n ', as would the moment curve for a simple beam. For this to be the case the negative area in... curve (b) must be decreased and the positive area increased. To ac- complish this the reference axis must be lowered, thus making the constant larger than the value assumed, A\ . The method of obtaining the value of the constant that will make the positive area equal to the negative area in (b) is to draw O'X 1 the closing line of the funic- ular polygon in (c f ), then draw P'X in the vector polygon parallel to O'X 1 in the funicular polygon. Then through ART. 86] THE CONSTANT OF INTEGRATION 125 X draw the horizontal axis OX, giving XX' or 00' in (b) the true value of the constant.

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