# fully restrained beam

## Fixed-end moments of fully restrained beam

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**

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

$M_B = -\dfrac{Pa^2b}{L^2}$

Value of EIy

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

Note: only for b > a

## Problem 737 | Fully restrained beam with one support settling

**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/L^{2}.

## Problem 736 | Shear and moment diagrams of fully restrained beam under triangular load

**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 734 | Restrained beam with uniform load over half the span

**Problem 734**

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

## Problem 730 | Uniform loads at each end of fully restrained beam

**Problem 703**

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

## Problem 729 | Uniform load over the center part of fixed-ended beam

## Problem 727 | Fully restrained beam with uniform load over the entire span

**Problem 727**

Repeat Problem 726 assuming that the concentrated load is replaced by a uniformly distributed load of intensity w_{o} over the entire length.

## Problem 726 | Fully restrained beam with concentrated load at midspan

**Problem 726**

A beam of length L, perfectly restrained at both ends, supports a concentrated load P at midspan. Determine the end moment and maximum deflection.

## Application of Area-Moment Method to Restrained Beams

See deflection of beam by moment-area method for details.

Rotation of beam from A to B

Deviation of B from a tangent line through A