1. A simply supported girder has a span of 12 metres. A 27 kN wheel load moves from one end to the other end on the span of the girder. Find the maximum bending moment which can occur at a section 4 metres from the left end.

2. A three-hinged parabolic arch of span L and rise h carries a uniformly distributed load of w per unit run over the whole span.

Show that

the horizontal thrust is wL^2/8h ,and

the arch is not subjected to any bending moment at any section.

3. Compare the strain energy of the two bars as shown in Figure 1. D is the diameter.

<img src='./qimages/14282-3.jpg'>

4. A long column fixed at one end and hinged at the other is 150 cm long and has a solid rectangular section. Calculate the depth of the section, if it is 10 cm wide. Euler's crippling load is 30000 N. Assume E 106 N/cm^2.

5. Analyse the continuous beam shown in Figure 2 by slope deflection method. The beam is of constant section throughout its length and supports remain at same level after loading.

<img src='./qimages/14282-5.jpg'>

6. Analyse the portal frame shown in Figure 3 by moment distribution method. The frame is fixed at A and D and has rigid joints at Band C. Draw the bending moment diagram.

<img src='./qimages/14282-6.jpg'>

Figure 3

Show that the shape factor for a circular section is 1.7.

A fixed beam of span L carries a uniformly distributed load w (total load) on the left half as shown in Figure 4. The plastic moment of resistance of the beam is Mp. Show that the value of collapse load is 14.2 Mp L.

<img src='./qimages/14282-7b.jpg'>

8. A cantilever has prop P at a distance L from the fixed end and on this length there is a uniformly distributed load w per unit run. If the prop is rigid and holds its point of application on the horizontal, find the reaction RA on the prop as shown in Figure 5.

<img src='./qimages/14282-8.jpg'>