Engineering Mathematics

fixed-ended beam

Problem 885 | Continuous Beam by Moment Distribution Method

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

825-continuous-beam.gif

 

Problem 855 | Continuous Beams with Fixed Ends

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

855-i-span.gif

 

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 | Continuous Beams with Fixed Ends

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

854-i-span.gif

 

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 | Continuous Beams with Fixed Ends

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.)
 

853-shear-diagram.gif

 

Problem 852 | Continuous Beams with Fixed Ends

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

852-fixed-ended-continuous-beam.gif

 

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 | Continuous Beams with Fixed Ends

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.
 

851-imaginary.gif

 

Problem 850 | Continuous Beams with Fixed Ends

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

850-fixed-ended-continuous-beam.gif

 

Problem 849 | Continuous Beams with Fixed Ends

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

849-load-identified.gif

 

Problem 848 | Continuous Beams with Fixed Ends

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

848-imaginary-spans.gif