Problem 425 Beam loaded as shown in Fig. P-425.
The vertical shear at C in the figure shown in previous section (also shown to the right) is taken as $V_C = (\Sigma F_v)_L = R_1 - wx$
where R1 = R2 = wL/2
$V_c = \dfrac{wL}{2} - wx$
The moment at C is $M_C = (\Sigma M_C) = \dfrac{wL}{2}x - wx \left( \dfrac{x}{2} \right)$
$M_C = \dfrac{wLx}{2} - \dfrac{wx^2}{2}$
If we differentiate M with respect to x: $\dfrac{dM}{dx} = \dfrac{wL}{2} \cdot \dfrac{dx}{dx} - \dfrac{w}{2} \left( 2x \cdot \dfrac{dx}{dx} \right)$
$\dfrac{dM}{dx} = \dfrac{wL}{2} - wx = \text{shear}$
thus,
Problem 422 Write the shear and moment equations for the semicircular arch as shown in Fig. P-422 if (a) the load P is vertical as shown, and (b) the load is applied horizontally to the left at the top of the arch.
Problem 421 Write the shear and moment equations as functions of the angle θ for the built-in arch shown in Fig. P-421.
Problem 420 A total distributed load of 30 kips supported by a uniformly distributed reaction as shown in Fig. P-420.
Problem 419 Beam loaded as shown in Fig. P-419.
Problem 418 Cantilever beam loaded as shown in Fig. P-418.
Problem 417 Beam carrying the triangular loading shown in Fig. P-417.
Problem 416 Beam carrying uniformly varying load shown in Fig. P-416.
Cantilever beam loaded as shown in Fig. P-415.
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