# Reactions of Continuous Beams | Shear Diagrams

# Problem 827 | Continuous Beam by Three-Moment Equation

# Problem 826 | Continuous Beam by Three-Moment Equation

# Problem 825 | Continuous Beam by Three-Moment Equation

# Problem 824 | Continuous Beam by Three-Moment Equation

**Problem 824**

The first span of a simply supported continuous beam is 4 m long, the second span is 2 m long and the third span is 4 m long. Over the first span there is a uniformly distributed load 2 kN/m, and over the third span there is a uniformly distributed load of 2 kN/m. At the midpoint of the second span, there is a concentrated load of 10 kN. Solve for the moment over the supports and check your answers using Problems 820 and 821.

# Problem 823 | Continuous Beam by Three-Moment Equation

**Problem 823**

A continuous beam simply supported over three 10-ft spans carries a concentrated load of 400 lb at the center of the first span, a concentrated load of 640 lb at the center of the third span and a uniformly distributed load of 80 lb/ft over the middle span. Solve for the moment over the supports and check your answers using the results obtained for Problems 819 and 822.

# Problem 822 | Continuous Beam by Three-Moment Equation

**Problem 822**

Solve Prob. 821 if the concentrated load is replaced by a uniformly distributed load of intensity w_{o} over the middle span.

Answers:

$M_2 = -\dfrac{w_o L^2}{4} \cdot \dfrac{1 + 2\beta}{4(\alpha + 1)(1 + \beta) - 1}$

$M_3 = -\dfrac{w_o L^2}{4} \cdot \dfrac{1 + 2\alpha}{4(1 + \alpha)(1 + \beta) - 1}$