Structural Engineering and Construction

Situation
Given:

1. The beam is simply supported on a span of 5 m, and carries the following loads:
   Superimposed Dead Load = 16 kN/m
   Live Load = 14 kN/m

   What is the maximum moment, M_u (kN·m), at ultimate condition? $U = 1.4D + 1.7L$

   A.   144	C.   104
   B.   158	D.   195

2. Find the number of 16 mm diameter bars required if the design moment at ultimate loads is 200 kN·m.

   A.   2	C.   6
   B.   4	D.   8

3. If the beam carries an ultimate concentrated load of 50 kN at midspan, what is the number of 16 mm diameter bars required?

   A.   2	C.   4
   B.   3	D.   5

Situation
The total length of the beam shown below is 10 m and the uniform load $w_o$ is equal to 15 kN/m.
 

1.   What is the moment at midspan if x = 2 m?

2.   Find the length of overhang x, so that the moment at midspan is zero.

3.   Find the span L so that the maximum moment in the beam is the least possible value.

Situation
The solid pole shown in the figure is loaded with a vertical load P = 25 kN and lateral load H = 0.95 kN. The pole is 3 m high, 300 mm diameter and weighs 22 kN/m³.
 

Situation
The three-hinged arch shown below is loaded with symmetrically placed concentrated loads as shown in the figure below.
 

The loads are as follows:
$$P_1 = 90 ~ \text{kN} \qquad P_2 = 240 ~ \text{kN}$$
 

The dimensions are:
$$H = 8 ~ \text{m} \qquad S = 4 ~ \text{kN}$$
 

Calculate the following:
 

1.   The horizontal reaction at A.

2.   The total reaction at B.

3.   The vertical reaction at C.

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.

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

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

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.

Situation
A beam 100 mm × 150 mm carrying a uniformly distributed load of 300 N/m rests on three supports spaced 3 m apart as shown below. The length x is so calculated in order that the reactions at all supports shall be the same.
 

1.   Find x in meters.

2.   Find the moment at B in N·m.

3.   Calculate the reactions in Newton.