Assessment available from: 9.00am XXXday xx May 2021

Latest submission time: 9.00am XXXday xx May 2021

All timings are given in British Summer Time (BST)

Between these times you must complete and submit your completed assessment.

This is an open book examination. You may refer to your own course and revision notes and look up information in offline or online resources, for example textbooks or online journals.    However, you may not communicate with any person or persons about this assessment       before the submission deadline unless explicitly permitted to do so in the instructions below. When you submit your assignment, you will be asked to agree to an academic integrity         declaration and confirm the work is your own. The use of the work of others, and your own   past work, must be referenced appropriately where this is relevant.  It is expected that you    will have read and understood the Regulations for Students and your programme handbook, including the references to and penalties for unfair practices such as plagiarism, fabrication  or falsification.

Which questions should be answered: Answer all questions

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

Submitting your assessment: You must submit your work in PDF format as a single file  for each question, uploaded to inspera. Your PDF document should be legible, with all  pages upright and in order. If you do not have a scanner available, please follow these     instructions for creating a PDF file on a mobile device:http://teachinghub.bath.ac.uk/wp-     content/uploads/2020/04/Scanning-from-Mobile-Devices.pdf. Additional guidance on how to submit your assessment is available at:https://teachinghub.bath.ac.uk/teaching-online-

options-and-considerations/support-for-students-alternative-assessment/

1. (42 marks)

a) For the beam shown in Figure 1 (a), draw the shear force and bending moment diagram, indicating values at salient points. (4 marks)

Figure 1a

b) Assuming the beam is steel with a cross-section as shown in Figure 1 (b), draw an elevation of the beam indicating five locations where it would be sensible to consider calculating principal stresses. For each location, write a sentence explaining why you have chosen that location. (5 marks)

Figure 1b

c) Calculate the maximum principal compressive stress at the web/flange junction at the positions of maximum sagging and hogging bending moment locations. State     whether you think these stresses are acceptable or not, with a sentence explaining  why. (9 marks)

d) It is decided to add a reinforced concrete slab on top of the beam, to act             compositely as shown in figure 1 (c). Making sensible assumptions about the         concrete acting in tension or compression, and assuming Young’s modulus of the  concrete is 20GPa, calculate the second moment of area of the section when used (i) in a sagging region and (ii) in a hogging region. (10 marks)

Figure 1c

e) Assuming a constant second moment of area for the whole beam equal to that in the sagging region, calculate the deflection in the middle of the 8m span. Do you     think this is a conservative or unconservative estimate of the maximum deflection? Give two reasons (bullet points) explaining why you think this. (6marks)

f) The composite action between the steel section and the concrete is provided by   the use of shear connectors (a steel stud welded to the top flange of the steel beam and embedded into the concrete). Each shear connector can carry 25kN of force in shear. What is the maximum spacing of shear studs required to provide composite  action? (4 marks)

g) For the composite section, calculate the maximum compressive stresses in the  concrete and steel due to the bending moments. Explain , in one sentence, whether or not these stresses are acceptable. (4 marks)

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2. (31 marks)

A 1m long steel channel section cantilever beam is shown in Figure 2 (a) (as 3- dimensional view and a cross section).

Figure 2a

a) Calculate the position of the centroid of this section. (2 marks)

b) The cantilever is loaded vertically through its centroid, rather than through its       shear centre, with a load of 40kN at the end of the cantilever, resulting in a torque    being applied. What is the angle of twist at the tip of the cantilever due to this torque (assume G = 77GPa)? (6 marks)

c) What is the maximum shear stress in the beam, considering both vertical shear    and torsion combined? Comment on whether this is an acceptable level of stress. (6 marks)

d) It is decided that the beam twists too much. A 5mm plate is welded, using an 8mm fillet weld, between the free edges of the two flanges, forming a box section, as         shown in figure 2(b). If the load remains applied at the same location as in part b,      making sensible assumptions about the cross section, how much does the section    twist now? What is the maximum shear stress due to torsion now? Comment , in one sentence, on your results. (7 marks)

e) At the support point, considering the shear stresses due to both vertical shear and torque, and the stresses due to bending what is the maximum compressive principal stress in the 5mm plate at the position of the weld (18mm from the bottom of the       section)? Comment on your result. (10 marks)

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3. (14 marks)

A pair of channel sections (each 75mm wide x 150mm deep, 5mm thick) are fixed   together, to form a beam of cross section as shown in Figure 3. The beam is simply supported and spans 3m. It is loaded with a vertical downwards UDL of 5kN/m        length and carries a horizontal wind UDL 1kN/m length, applied from the left of the  section. What is the maximum compressive and tensile stress in the section? (14    marks)

Figure 3

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