fixed-ended beam

Problem 885
Solve for the support moments in Problem 825 if the ends are perfectly fixed instead of simply supported.
 

Problem 883
Compute the moments over the supports of the beam shown in Fig. P-853.
 

Problem 855
If the distributed load in Prob. 854 is replaced by a concentrated load P at midspan, determine the moments over the supports.
 

Answers:
$M_1 = \dfrac{PL}{8} \cdot \dfrac{1}{\alpha + 2} = M_4$

$M_2 = -\dfrac{PL}{8} \cdot \dfrac{2}{\alpha + 2} = M_3$
 

Problem 854
Solve for the moment over the supports in the beam loaded as shown in Fig. P-854.
 

Answers:
$M_1 = \dfrac{w_o L^2}{12} \cdot \dfrac{1}{\alpha + 2} = M_4$

$M_2 = -\dfrac{w_o L^2}{12} \cdot \dfrac{2}{\alpha + 2} = M_3$
 

Problem 853
For the continuous beam shown in Fig. P-853, determine the moment over the supports. Also draw the shear diagram and compute the maximum positive bending moment. (Hint: Take advantage of symmetry.)
 

Problem 852
Find the moments over the supports for the continuous beam in Figure P-852. Use the results of Problems 850 and 851.
 

Answers
$M_1 = -146.43 ~ \text{N}\cdot\text{m}$

$M_2 = -307.14 ~ \text{N}\cdot\text{m}$

$M_3 = -521.43 ~ \text{N}\cdot\text{m}$
 

Problem 851
Replace the distributed load in Problem 850 by a concentrated load P at the midspan and solve for the moment over the supports.
 

Problem 850
Determine the moment over the supports for the beam loaded as shown in Fig. P-850.
 

Problem 849
Find the moments over the support for the beam shown in Fig. P-849.
 

Problem 848
Determine the support moments and reactions for the beam shown in Fig. P-848.