Assessment available from: 9.00am Monday 11 May 2020

Latest submission time: 10.00am Friday 29 May 2020

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Which questions should be answered: Answer all questions

Additional materials needed to complete the assessment: Calculators may be used

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A  new  bridge  is  being  planned  across  a  valley  in  the  Midlands  in England.  The  bridge  is  to  carry  a  new  railway  line  to  encourage enhanced use of public transport, and its total length is to be about 800m. The bridge will have a concrete deck, which will rest on concrete columns (bridge piers), each spaced about 100m apart.

(a)    What are some of the key ethics-related  issues which the client and

engineers should consider during the decision-making process for this bridge, particularly when set in the context of our climate emergency?  [4 marks]

(b)    Based on the issues which have been covered in this unit, write down

the most important structural design checks which you think should be conducted to ensure that the bridge deck and bridge piers are safe and functional. Do not attempt to carry out any calculations at all.                       [4 marks]

2      (a)    Without  carrying  out  any  calculations  at  all,  demonstrate  that  the

vertical deflection at mid-span  in each of the following  beams  is the same if each has the same value of EI.              [5 marks]

100kN

6m                          

Figure 2(a) Asymmetrically-loaded beam

50kN

50kN

4m

Figure 2(b) Symmetrically-loaded beam

(b)    The beams above are both made of steel, and the cross section of each

is shown in Figure 2(c). Note that the beam is not symmetrical about its

centroidal  axis .  Calculate  the  Second  Moment  of Area  of this  cross section.         [7 marks]

10         

100

Figure 2(c) Cross section of steel beam

(c)   Calculate the mid-span vertical deflection of the beam shown in Figure 2(a). You may refer to the relevant example in your lecture notes as the basis of your answer.

(d)   For the  beam  in  Figure  2(a),  calculate the  maximum  compressive bending stress in the cross section at the location of maximum bending, and comment on its magnitude. Provide one easy solution to reduce the compressive bending stress without adding any additional material, moving the load or changing the span.

(e)    The engineer decides to make the beam in Figure 2(a) continuous by

adding  a  support  at  mid-span,  as  shown  in  Figure  2(d).  Sketch the

deflected shape of this structure. From this sketch, estimate the position of the point of contraflexure along the beam. Sketch the approximate bending moment diagram, showing salient approximate values.

100kN

Figure 2(d) Continuous steel beam

(f)     Now use the result from part 2(c) above to calculate the vertical reaction

at  the  central  support,  and  hence  draw  the  ‘real’  bending  moment diagram for this beam, showing salient values. Compare your results

with the approximate results in part 2(e), and comment on your findings.    [ 10 marks]

A steel bridge in Iceland is made up of many hollow-section beams, each placed next to each other to create a wide bridge. One such   beam is shown in Figure 4. The thickness of the steel is 20mm       throughout. The beams are continuous over many supports. Each   beam has a Second Moment of Area I = 780x106mm4 , and is       expected to experience the following actions at its critical section:

M  =  590 kNm

S   =  520 kN

T   =  410 kNm

1000

600

Figure 4 Cross section of each hollow steel beam

(a)    For the purposes of calculating the torsional shear stress in this beam

structure, would you consider this section to be open or closed? Based on your assumption, determine approximately the maximum torsional   shear stress.

(b)    Determine the normal compressive stress at the junction between the

top flange and the webs due to bending. The distance between the top flange junction and the neutral axis is 120mm. Determine the shear     stress at the same location due to the vertical shear force. Make any   assumptions about dimensions which you feel are necessary and         appropriate.

(c)    Hence, by combining your results from (a) and (b), calculate the          principal stresses at the junction between the top flange and the webs, and comment on whether you think they are within acceptable limits    using your engineering judgement.

(d)    The bridge was built in mid-winter when the temperature was -50ºC. In mid-summer, the ends of the beam are held fast and the temperature   of the entire member increases by 70ºC compared with the original      ambient construction temperature. All other applied loading remains as it was prior to the temperature increase. How will this temperature        increase affect the principal stresses calculated in part (c) above? Will

it make the bridge more or less susceptible to buckling issues? Do not carry out any calculations.

5     (a)    Sketch feasible bending moment diagrams for the following three

frames shown in Figure 5(a). Note that where a pin is not shown, the

connection is of full fixity.                                                                                      [ 10 marks]

w                                           w

(a)                                                 (b)

w

(c)

Figure 5(a) Portal frames of varying fixity

The engineer who is deciding which of the frames above to choose for her design is concerned by the potential for the columns to buckle. She decides to choose the fully-fixed option for her design, shown below in Figure 5(b), but now showing the vertical loading (12MN in each column) which it will resist from multiple-floor loading above it. Every column is braced out of plane and these frames cannot sway laterally because they are tied into a stability core system.

12MN

4m

Figure 5(b) Portal frames of varying fixity

(b)    The columns are square hollow steel sections of outer side dimension

200mm and chunky wall thickness 50mm. Each column is 4m in length. By making two distinct, sensible assumptions about the possible fixity conditions at the top of each column, determine whether you think the

engineer should inform the client that the columns are susceptible to buckling or not.

(c)    A strain gauge is placed on one of the columns, reading the axial strain in the column. What reading might you expect it to have under the loading shown in Figure 5(b)?        [5 marks]