three-moment equation

Continuous Beam With Equal Support Reactions

Situation
A beam 100 mm × 150 mm carrying a uniformly distributed load of 300 N/m rests on three supports spaced 3 m apart as shown below. The length x is so calculated in order that the reactions at all supports shall be the same.
 

design-practice-2-given.png

 

1.   Find x in meters.

A.   1.319 C.   1.217
B.   1.139 D.   1.127

2.   Find the moment at B in N·m.

A.   -240 C.   -242
B.   -207 D.   -226

3.   Calculate the reactions in Newton.

A.   843.4 C.   863.8
B.   425.4 D.   827.8

 

Problem 872 | Continuous Beam with Spring End-Support

Problem 872
Repeat Problem 871 assuming the loadings on the spans are interchanged.
 

Problem 871 | Continuous Beam with Spring End-Support

Problem 871
The continuous beam in Figure P-871 is supported at its left end by a spring whose constant is 300 lb/in. For the beam, E = 1.5 × 106 psi and I = 115.2 in.4. Compute the load on the spring and its deflection.
 

871-continuous-beam-spring-support.gif

 

Problem 867 | Deflection by Three-Moment Equation

Problem 867
For the beam in Figure P-867, compute the value of P that will cause a zero deflection under P.
 

867-simple-beam-varying-load-overhang.gif

 

Problem 860 | Deflection by Three-Moment Equation

Problem 860
Determine the value of EIδ at the end of the overhang and midway between the supports for the beam shown in Fig. P-860.
 

860-overhang-beam-given.gif

 

Deflections Determined by Three-Moment Equation

Problem 859
Determine the value of EIδ under P in Fig. P-859. What is the result if P is replaced by a clockwise couple M?
 

859-overhang-with-concentrated-load.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 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

 

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