concentrated load

Problem 832
Refer to Problem 824.
 

Problem 830
Refer to Problem 815.
 

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

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