Continuous Beams

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.
 

Problem 818
In Problem 817, determine the changed value of the applied couple that will cause M₂ to become zero.
 

Problem 817
Find the moment under the support R₂ of the continuous beam shown in Fig. P-817.
 

Problem 816
Determine the lengths of the overhangs in Fig. P-816 so that the moments over the supports will be equal
 

Problem 815
Find the moment at R₂ and R₃ of the continuous beam shown in Fig. P-815.
 

Problem 814
Find the moment at R₂ of the continuous beam shown in Fig. P-814.