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

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

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

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

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

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

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

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

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).

2.   Calculate the maximum tensile stress (MPa).

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

Problem
A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

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.

Problem
A conical tank in upright position (vertex uppermost) stored water of depth 2/3 that of the depth of the tank. Calculate the ratio of the volume of water to that of the tank.

Problem
A +0.8% grade meets a -0.4% grade at km 12 + 850 with elevation 35 m. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.