Engineering Mechanics Assessment Brief

·Attempt all questions

·To pass this assignment, you must achieve a mark of 40% for the whole assessment

·Only HAND-WRITTEN submission will be accepted.

·All questions are equally weighted and marked on the percentage scale

·Show all stages of your work

·Late submissions will not be accepted and a grade of 0NS awarded

·Check your work carefully for inaccurate spelling, punctuation and grammar

·Please mark your submission for the attention of Dr Georgios Papavasileiou.

Assessment Brief

Students who have failed the exam component of the assessment must resubmit this. The scope of this assessment includes solving 4 questions in relation to engineering mechanics. All questions must be attempted and a mark of 40% for the whole assessment should be achieved.

Your submission must be a single PDF file, containing all the answers to the questions, and a single LinPro model file.

Your working may be hand-written only. Extracts/Screenshots from software can be attached as images, but they do not substitute hand calculations where they are required. Make sure that all numerical results required on the exam paper are in it. Do not just attach separate image files to your submission.

You need to ensure that the images are appropriately scaled and rotated. Inappropriately attached images will not be assessed.

Answers not justified by calculations will not receive any marks.

Q1 (a) In a continuous beam with three equal spans, fixed at one end and free at the other, subjected to a uniformly distributed load over its full length, where would you expect the maximum deflection to occur? You must support your answer with sketches and underpin your answer with the theory.

(b) Explain the relationship between bending moments and load distribution. Support your answer using appropriate mathematical formulation. 5%

(c) In the structure below, what is the value of the bending moment at point B? Explain why.

(d) What are the boundary conditions? Where are they used in the applications shown in this module? 5%

(e) Show the stress distribution on a Tee-section (T-shaped section) subjected to normal stresses only. If multiple states are possible, sketch them all and explain how they would be attained. 5%

(f) Explain what happens to an I-shaped section subject to a shear parallel to its flanges, passing from its centroid. 5%

Q2 (a) Consider you are dealing with a 5m long cantilever beam with a 500kN point load at mid-span. The beam is made of structural steel and must not exceed a deflection of 20mm. Find the minimum required second moment of area of the cross-sectional profile. 5%

Requirements for Passing

(b) Discuss what happens if the client decides that the beam from sub-question (a) must be made of aluminium instead of steel. If you believe, it is necessary, present new calculations 5%

(c) For the previous beams, propose a solid circular section that meets the deflection limit. 5%

(d) Considering sustainability, discuss what would happen if it is decided to use a 25 x 25 cm square section in the above beams. 5%

(e) Find the maximum deflection of a 5m long simply-supported beam subjected to a 10kN/m UDL and 100kN point load at the mid-span. You must sketch the structural arrangement and include the deflection shape. Leave your answer as a function of EI. 5%

(f) Discuss and compare the deflection behaviour of a cantilever and a propped cantilever. Assume that both the cantilever and propped cantilever have the same length, its cross-section is rectangular and are subjected to a point load. You must underpin your explanation with the theory, sketches, include relevant equations, decide a material and cross-section size and present calculations for the variables you decide to assume. 5%

Q3 Find the maximum deflection and maximum bending moment in the continuous beam shown in Figure 1. You must accompany your calculations with a detailed description of what you are doing and present relevant sketches where necessary.

Find the maximum stress in MPa at the most severely loaded section of the beam and present a detailed sketch of the stress distribution. Assume a UKB 457x191x82

Q4 (a) You are required to model the structure shown in Figure 2 in LinPro software:

The variables of the structure are: (a) the number of cables at each side of the tower (n), (b) the deck span between consequent supports (between cable-deck joints), and (c) the height of the tower above the deck. Calculate the aforementioned based on the last 3 digits of your student number as follows:

Number of cables (n) based on the last digit of your student number 0, 1 5 cables

Deck span between consequent supports (L), based on the penultimate digit of your student number 0, 1 5m span

Height of cable tower above deck (H) based on the third from last digit of your student number 0, 1 20m

For example, if your student number is 1234567890, your model should have (a) 5 cables, (b) 9m spacing between cable-deck connections and (c) 40m high towers.

To answer this question, you need to (a) submit the model file from LinPro, and (b) explain the modelling assumptions made.

Guidance on modelling in LinPro is available on Canvas under the module titled ‘LinPro’, as well as in the lecture where the software was presented.

The software LinPro is available for download at AppsAnywhere (https://appsanywhere.wlv.ac.uk/). 10%

(b) I.What is the type of structure shown in Fig. 2?

II.Which loads/actions should be considered for the design of this structure?

III.Discuss potential health and safety issues that might occur during construction of this structure.

IV.Explain how one could calculate the internal forces in each of the elements of the structure. You do not need to perform any calculations but you need to show the mathematical formulation when this is necessary. 10%