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DEPARTMENT OF ARCHITECTURE & CIVIL ENGINEERING

AR10370

STRUCTURES 1B

1 (a) The planar block of brittle material shown in figure 1(a) is loaded along

each of its edges in a laboratory test, creating a plane stress situation of pure shear in the material. By considering Mohr’s Circle for this stress state, show qualitatively that the material should theoretically crack in

tension along 45O diagonals, as shown. [4 marks]

Figure 1(a) State of pure shear

(b) A continuous beam is made up of similar brittle material and loaded as

shown in figure 1(b). A strain gauge rosette is placed on the beam at a specific location, from which the state of stress shown in figure 1(c) is found. Indicate on a diagram of the beam where the possible locations

(broadly speaking) for the strain gauge rosette could be. [6 marks]

Figure 1(b) Continuous beam

122MPa

194MPa

Figure 1(c) Stress state at a particular point

[5 marks]

A student on an Engineers Without Borders placement has been asked to build a disaster-relief temporary footbridge across a stream, of span 11m, as shown in Figure 2(a). All she has available to her is some old steel railway track. The cross section of the railway track is shown in Figure 2(b). Her first thought is to simply lay the steel railway tracks across the span, as shown in Figure 2(a). In order to check that her design is adequate, she assumes that each railway track beam will take a maximum point load of 70kN at midspan, which allows conservatively for self weight and the most onerous imposed loading to which each railway track beam might be exposed.

(a) What is the Second Moment of Area of the railway track?

(b) Explain how she would calculate the maximum shear stress at the

most critical cross section. Do not carry out any calculations.

(d) How might she reduce the compressive bending stress in this cross section without adding any additional structural material?

70kN

11m

Figure 2(a) Simply-supported bridge span

60 120 60

120

R = 60

Figure 2(b) Cross section of railway track (dimensions in mm)

The planar truss structure shown in Figure 3 is braced out of plane. The structure carries a vertical load of 150kN at point A, as shown. Every member is a steel square hollow section of outer side dimension 60mm and wall thickness 4mm. All diagonals in the truss are at 45° . By equating external work done by the vertical load to internal stored elastic strain energy, determine the vertical displacement of the joint at

point A. [10 marks]

150kN

3m	3m

Figure 3 Planar truss

4 (a) W hat is the most important aspect that you learned from the timber beam

laboratory test as part of Structures 1b, and why was the apparent measurement of Poisson’s Ratio out of line with the limits on its

theoretical value? [5 marks]

(b) What is the most important aspect that you learned from the shear centre

laboratory test as part of Structures 1b, and why did the three values for

‘e’ not coincide with each other? [4 marks]

5 The cantilevered beam in Figure 4(a) is loaded as shown. It is made of steel, and has a prismatic cross section with a second moment of area of 575x106 mm4 . Ignore self weight.

(a) What is the approximate deflection at the tip of the cantilever?

(b) What is the maximum hogging moment in this beam?

30kN/m

3m	4m

Figure 4(a) Cantilevered beam

(c) A prop support is now inserted at the right hand end of this beam, as shown in Figure 4(b). By using your result above, what is the value of the reaction at the right hand support?

(d) What is the new maximum hogging moment in this beam? Comment on the result compared with the unpropped case above.

(e) Sketch the deflected shape of this propped structure.

30kN/m

3m	4m

6 Redraw each of the following beam cross sections in your answer booklet. It is to be assumed that the beam which each of these cross sections represent is being loaded vertically downwards through its centroid along its length giving rise to My only, where ‘y’ is the horizontal axis.

(a) For each cross section, sketch the likely position and inclination of the

neutral axis. Do not carry out any calculations in answering this

question, and sketch neatly. [8 marks]

(b) On each of the sketches above, add the vector direction in which the

cross section will attempt to move. [8 marks]

(a)

(d)

(f)

(g)

(h)

Figure 5 Eight beam cross sections

7	Lateral torsional buckling is a phenomenon which can occur in thin- walled beams where the force in the compression flange leads to this flange suddenly buckling sideways. You have been asked to conduct a rough check for lateral torsional buckling of the steel beam shown in elevation in Figure 6(a) and in section in Figure 6(b). Two of your key assumptions should be that the cross section can be approximated as only consisting of the two flanges (the thin web should be assumed to carry none of the bending), as shown in Figure 6(c), and that if lateral torsional buckling occurred, then the top compression flange would buckle laterally into the shape shown in plan in Figure 6(d). Note that the compression flange is restrained laterally at all load and support points. (a) What is the bending moment in the middle 20m of the beam? (b) By assuming the cross section in Figure 6(c), what then is the approximate compression force in the top flange? (c) Is there a danger that this beam might undergo lateral torsional buckling? Explain your answer.
		[2 marks]
		[3 marks]
		[5 marks]