CE Board November 2018

Velocity of Separation: How fast is the distance between two cars changing?

Problem
A Toyota Land Cruiser drives east from point A at 30 kph. Another car, Ford Expedition, starting from B at the same time, drives S30°W toward A at 60 kph. B is 30 km from A. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.

A.   70 kph C.   55 kph
B.   80 kph D.   60 kph

 

Simply Supported Beam with Support Added at Midspan to Prevent Excessive 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

 

Limit the Deflection of Cantilever Beam by Applying Force at the Free End

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

 

2018-nov-design-cantilever-beam-given.jpg

 

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

 

Support Added at the Midspan of Simple Beam to Prevent Excessive Deflection

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, Ix = 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 = 4 m
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

 

Stresses of Hollow Circular Tube Used as a Pole

Situation
A 12-m pole is fixed at its base and is subjected to uniform lateral load of 600 N/m. The pole is made-up of hollow steel tube 273 mm in outside diameter and 9 mm thick.
1.   Calculate the maximum shear stress (MPa).

A.   0.96 C.   1.39
B.   1.93 D.   0.69

2.   Calculate the maximum tensile stress (MPa).

A.   96.0 C.   60.9
B.   69.0 D.   90.6

3.   Calculate the force (kN) required at the free end to restrain the displacement.

A.   2.7 C.   27
B.   7.2 D.   72

 

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