fixed-end moment

The Moment Distribution Method

Moment distribution is based on the method of successive approximation developed by Hardy Cross (1885–1959) in his stay at the University of Illinois at Urbana-Champaign (UIUC). This method is applicable to all types of rigid frame analysis.
 

008-carry-over-moment.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

 

Fixed-end moments of fully restrained beam

Summary for the value of end moments and deflection of perfectly restrained beam carrying various loadings. Note that for values of EIy, y is positive downward.
 

Case 1: Concentrated load anywhere on the span of fully restrained beam

000-fully-restrained-beam-point-load.gifEnd moments
$M_A = -\dfrac{Pab^2}{L^2}$

$M_B = -\dfrac{Pa^2b}{L^2}$
 

Value of EIy
$\text{Midspan } EI\,y = \dfrac{Pb^2}{48}(3L - 4b)$

Note: only for b > a

 

Problem 738 | Fully restrained beam with moment load

Problem 738
A perfectly restrained beam is loaded by a couple M applied where shown in Fig. P-738. Determine the end moments.
 

738-moment-load-fixed-ended-beam.gif

 

Solution 738

Problem 737 | Fully restrained beam with one support settling

Problem 737
In the perfectly restrained beam shown in Fig. P-737, support B has settled a distance Δ below support A. Show that MB = -MA = 6EIΔ/L2.
 

737-restrained-beam-with-settling-support.gif

 

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