Engineering Mathematics

Beam Deflection

Continuous Beam With a Gap and a Zero Moment in Interior Support

Situation
A beam of uniform cross section whose flexural rigidity EI = 2.8 × 1011 N·mm2, is placed on three supports as shown. Support B is at small gap Δ so that the moment at B is zero.
 

design-practice-1-given.gif

 

1.   Calculate the reaction at A.

A.   4.375 kN C.   5.437 kN
B.   8.750 kN D.   6.626 kN

2.   What is the reaction at B?

A.   4.375 kN C.   5.437 kN
B.   8.750 kN D.   6.626 kN

3.   Find the value of Δ.

A.   46 mm C.   34 mm
B.   64 mm D.   56 mm

 

Problem 870 | Beam Deflection by Three-Moment Equation

Problem 870
Compute the value of EIδ at the overhanging end of the beam in Figure P-870 if it is known that the wall moment is +1.1 kN·m.
 

870-propped-beam-with-overhang.gif

 

Problem 869 | Deflection by Three-Moment Equation

Problem 869
Find the value of EIδ at the center of the first span of the continuous beam in Figure P-869 if it is known that M2 = -980 lb·ft and M3 = -1082 lb·ft.
 

869-continuous-beam.gif

 

Problem 868 | Deflection by Three-Moment Equation

Problem 868
Determine the values of EIδ at midspan and at the ends of the beam loaded as shown in Figure P-868.
 

868-simple-overhanging-beam-triangular-load.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

 

Solution to Problem 696-697 | Beam Deflection by Method of Superposition

Problem 696
In Fig. P-696, determine the value of P for which the deflection under P will be zero.
 

Solution to Problem 693 | Beam Deflection by Method of Superposition

Problem 693
Determine the value of EIδ at the left end of the overhanging beam in Fig. P-693.
 

Solution to Problem 689 | Beam Deflection by Method of Superposition

Problem 689
The beam shown in Fig. P-689 has a rectangular cross section 4 inches wide by 8 inches deep. Compute the value of P that will limit the midspan deflection to 0.5 inch. Use E = 1.5 × 106 psi.
 

Solution to Problem 688 | Beam Deflection by Method of Superposition

Problem 688
Determine the midspan value of EIδ at the left end of the beam shown in Fig. P-688.
 

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