three-moment equation

Problem 835
Refer to Problem 827 for which M₂ = -1215 lb·ft and M₃ = -661 lb·ft.
 

Problem 834
Refer to Problem 826.
 

Problem 833
Refer to Problem 825 for which M₂ = -980 lb·ft and M₃ = -1082 lb·ft.
 

Problem 832
Refer to Problem 824.
 

Problem 831
Refer to Problem 817 for which M₂ = -180 lb·ft.
 

Problem 830
Refer to Problem 815.
 

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.