Beam Deflection

Situation
A simply supported beam has a span of 12 m. The beam carries a total uniformly distributed load of 21.5 kN/m.
1. To prevent excessive deflection, a support is added at midspan. Calculate the resulting moment (kN·m) at the added support.

A. 64.5	C. 258.0
B. 96.8	D. 86.0

2. Calculate the resulting maximum positive moment (kN·m) when a support is added at midspan.

A. 96.75	C. 108.84
B. 54.42	D. 77.40

3. Calculate the reaction (kN) at the added support.

A. 48.38	C. 161.2
B. 96.75	D. 80.62

Situation
A cantilever beam, 3.5 m long, carries a concentrated load, P, at mid-length.

Given:
P = 200 kN
Beam Modulus of Elasticity, E = 200 GPa
Beam Moment of Inertia, I = 60.8 × 10⁶ mm⁴

1. How much is the deflection (mm) at mid-length?

A. 1.84	C. 23.50
B. 29.40	D. 14.70

2. What force (kN) should be applied at the free end to prevent deflection?

A. 7.8	C. 62.5
B. 41.7	D. 100.0

3. To limit the deflection at mid-length to 9.5 mm, how much force (kN) should be applied at the free end?

A. 54.1	C. 129.3
B. 76.8	D. 64.7

Situation
A simply supported steel beam spans 9 m. It carries a uniformly distributed load of 10 kN/m, beam weight already included.

Given Beam Properties:
Area = 8,530 mm²
Depth = 306 mm
Flange Width = 204 mm
Flange Thickness = 14.6 mm
Moment of Inertia, I_x = 145 × 10⁶ mm⁴
Modulus of Elasticity, E = 200 GPa

1. What is the maximum flexural stress (MPa) in the beam?

A. 107	C. 142
B. 54	D. 71

2. To prevent excessive deflection, the beam is propped at midspan using a pipe column. Find the resulting axial stress (MPa) in the column

Given Column Properties:
Outside Diameter = 200 mm
Thickness = 10 mm
Height, H = 4 m
Modulus of Elasticity, E = 200 GPa

A. 4.7	C. 18.8
B. 9.4	D. 2.8

3. How much is the maximum bending stress (MPa) in the propped beam?

A. 26.7	C. 15.0
B. 17.8	D. 35.6

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.

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.

Read more about Problem 870 | Beam Deflection by Three-Moment Equation
Add new comment
14877 reads

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.