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 |
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.
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.
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
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 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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Sum of Areas of Infinite Number of Squares
Problem
The side of a square is 10 m. A second square is formed by joining, in the proper order, the midpoints of the sides of the first square. A third square is formed by joining the midpoints of the second square, and so on. Find the sum of the areas of all the squares if the process will continue indefinitely.
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Problem
A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave toward the point of intersection of the two tangents. Each tangent and the arc of the circle is 1 mile long, what is the radius of the circle? Use 1 mile = 5280 ft.
| A. 1437 ft. | C. 1347 ft. |
| B. 1734 ft. | D. 1374 ft. |
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Sum of Areas of Equilateral Triangles Inscribed in Circles
Problem
An equilateral triangle is inscribed within a circle whose diameter is 12 cm. In this triangle a circle is inscribed; and in this circle, another equilateral triangle is inscribed; and so on indefinitely. Find the sum of the areas of all the triangles.
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