Statically Indeterminate pinned jointed frame

Question 1

Determine the forces in the members for the pinned jointed frame shown in Figure Question 1, using the method of virtual work. All members have the same EA.

Question 2

For the beam shown in Figure Question 2;

1. Determine the reaction at B using the method of virtual work,

2. Draw the shear force and bending moment diagrams showing prominent values.

3. Sketch the deflected shape.

The beam has a constant EI between A and B and varies linearly from EI at the support B to 2EI at the support C.

Question 3

A steel column is fixed at both ends for bending about the YY axis and pinned at both ends for bending about the XX axis. It has the following properties:

I_xx = 30 x 10⁶ mm⁴; I_yy = 15 x 10⁶ mm⁴

If the height of the column is 5.75m, determine the maximum buckling load that the column can carry.

Question 4

Figure Question 4 show a beam simply supported at A and C and free at D. Draw the influence-line diagrams for

• Reaction at C
• Bending moment at B
• Reaction at A
• Shearing force at B

Question 5

PRESTRESSED CONCRETE

Question 5a

It is required to design and construct a bridge to cross the valley shown in Figure Question 5(a). The carriageway on each side comprises the following:

• 2 No Lanes ( 3700 mm each)
• 3000 mm shoulder
• 1200 mm Inner Strip

Provide two concept designs as follows:

1) Prestressed (Pre-tensioned) concrete

2) Prestressed (Post-tensioned) concrete

The distance between supports (span) should be between 40 and 150m.

Provide sketches showing the longitudinal elevation and the typical cross section for each solution.

Question 5b

A rectangular beam of 200 mm wide and 425 mm depth is simply supported and has a span of 6 m. The variable action acting on the beam is 16 kN/m. If a straight tendon (for prestressing) is provided at an eccentricity of 75 mm below the centroid of the section, find:

1. the minimum prestress force necessary for no tension at mid-span under variable action.

2. the corresponding stresses under permanent action only at mid-span and at the end of the members