December 2012

Summary for the value of end moments and deflection of perfectly restrained beam carrying various loadings. Note that for values of EIy, y is positive downward.
 

Case 1: Concentrated load anywhere on the span of fully restrained beam

End moments
$M_A = -\dfrac{Pab^2}{L^2}$

$M_B = -\dfrac{Pa^2b}{L^2}$
 

Value of EIy
$\text{Midspan } EI\,y = \dfrac{Pb^2}{48}(3L - 4b)$

Note: only for b > a

Problem 737
In the perfectly restrained beam shown in Fig. P-737, support B has settled a distance Δ below support A. Show that M_B = -M_A = 6EIΔ/L².
 

Problem 736
Determine the end shears and end moments for the restrained beam shown in Fig. P-736 and sketch the shear and moment diagrams.
 

Problem 735
The beam shown in Fig. P-735 is perfectly restrained at A but only partially restrained at B, where the slope is w_oL³/48EI directed up to the right. Solve for the end moments.
 

Problem 734
Determine the end moments for the restrained beams shown in Fig. P-734.
 

Problem 733
The load P in Prob. 732 is replaced by a counterclockwise couple M. Determine the maximum value of M if the stress in the vertical rod is not to exceed 150 MPa.
 

Problem 732
The midpoint of the steel in Fig. P-732 is connected to the vertical aluminum rod. Determine the maximum value of P if the stress in the rod is not to exceed 120 MPa.
 

Problem 731
The beam shown in Fig. P-731 is connected to a vertical rod. If the beam is horizontal at a certain temperature, determine the increase in stress in the rod if the temperature of the rod drops 90°F. Both the beam and the rod are made of steel with E = 29 × 10⁶ psi. For the beam, use I = 154 in.⁴
 

Problem 703
Determine the end moment and maximum deflection for a perfectly restrained beam loaded as shown in Fig. P-730.