## Problem 870 | Beam Deflection by Three-Moment Equation

**Problem 870**

Compute the value of EIδ at the overhanging end of the beam in Figure P-870 if it is known that the wall moment is +1.1 kN·m.

**Problem 870**

Compute the value of EIδ at the overhanging end of the beam in Figure P-870 if it is known that the wall moment is +1.1 kN·m.

**Problem 869**

Find the value of EIδ at the center of the first span of the continuous beam in Figure P-869 if it is known that M_{2} = -980 lb·ft and M_{3} = -1082 lb·ft.

**Problem 868**

Determine the values of EIδ at midspan and at the ends of the beam loaded as shown in Figure P-868.

**Problem 866**

Determine the midspan value of EIδ for the beam shown in Fig. P-866.

**Problem 865**

For the beam shown in Fig. P-865, compute the value of EIδ at x = 6 ft and at the end of the overhang.

**Problem 864**

An 18-ft beam, simply supported at 4 ft from each end, carries a uniformly distributed load of 200 lb/ft over its entire length. Compute the value of EIδ at the middle and at the ends.

**Problem 863**

For the beam shown in Fig. P-863, determine the value of EIδ midway between the supports and at the left end.

**Problem 862**

Determine the value of EIδ at B for the beam shown in Fig. P-862.

**Problem 860**

Determine the value of EIδ at the end of the overhang and midway between the supports for the beam shown in Fig. P-860.

**Summary of key points**

- The three-moment equation can be applied at any three points in any beam. It will determine the relation among the moments at these points.
- The terms $6A\bar{a}/L$ and $6A\bar{b}/L$ refer to the moment diagram by parts resulting from the simply supported loads between any two adjacent points described in (1).
- The heights h
_{1}and h_{3}from the equation

$M_1L_1 + 2M_2(L_1 + L_2) + M_3L_2 + \dfrac{6A_1\bar{a}_1}{L_1} + \dfrac{6A_2\bar{b}_2}{L_2} = 6EI \left( \dfrac{h_1}{L_1} + \dfrac{h_3}{L_2} \right)$

refer to the respective vertical distance of points 1 and 3 from point 2. The height h is positive if above point 2 and negative if below it.