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 4 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.
 

824-continuous-beam.gif

 

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.
 

823-continuous-beam.gif

 

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 wo over the middle span.
 

822-beta-alpha-span-uniform-load.gif

 

Answers:
M2=woL241+2β4(α+1)(1+β)1

M3=woL241+2α4(1+α)(1+β)1