Sec. 1.8 HISTORICAL REMARKS 29 is loaded by a distributed lateral load of intensityp(x) per unit length (Fig. P1.8). Find an approximate expression for the deflection curve by assuming that it can be represented with sufficient accuracy by the expression N nxx u(x) = C a, sin - L n=l Note: This expression satisfies the end conditions for arbitrary coefficients a,. Use the minimum potential energy theorem. Consider a uniform cantilever beam clamped at 2 = 0 (Fig. P1.9). According to Bernoulli-Euler theory of beams, the differential equation .governing the deflection of the beam is 1.9. d2w- M dx2 EI' *2 123456 P1.9 where w is the deflection parallel to the z-axis and M is the bending moment at station x. This equation is valid if the beam is straight and slender and if
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