moment over the support

Problem 828 - Reactions of Continuous Beam
A continuous beam carries a uniform load over two equal spans as shown in Fig. P-828.
 

Problem 827
See Figure P-827.
 

Problem 826
See Figure P-826.
 

Problem 825
See Fig. P-825.
 

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.
 

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
Solve Prob. 821 if the concentrated load is replaced by a uniformly distributed load of intensity w_o over the middle span.
 

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

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

Problem 821
See Fig. P-821.
 

$M_2 = -\dfrac{3PL}{8} \cdot \dfrac{1 + 2\beta}{4(1 + \alpha)(1 + \beta) - 1}$           answer

$M_3 = -\dfrac{3PL}{8} \cdot \dfrac{1 + 2\alpha}{4(1 + \alpha)(1 + \beta) - 1}$           answer
 

Problem 820
Solve Prob. 819 if the concentrated load is replaced by a uniformly distributed load of intensity w_o over the first span.
 

Problem 819
Find the moment under the supports R₂ and R₃ for the beam shown in Fig. P-819.