UNIT 62: STRENGTHS OF MATERIALS Unit code: K/601/1409 QCF level: 5 Credit value: 15

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1 UNIT 62: STRENGTHS OF MATERIALS Unit code: K/601/1409 QCF level: 5 Credit value: 15 ASSIGNMENT - OUTCOME 1 TARGET SUBMISSION DATE:... NAME: I agree to the assessment as contained in this assignment. I confirm that the work submitted is my own work. Date Issued: Signature: Date submitted: This assignment will be used to grade the sections highlighted. PASS CRITERIA Outcome 1 Investigate engineering components which are subjected to complex loading systems Assessment Criteria for a pass analyse two-dimensional stress systems making appropriate use of Mohr's stress circle carry out experimental strain analysis using electrical resistance strain gauges Achieved apply the appropriate theory of elastic failure to loaded components to determine operational factors of safety OUTCOME 2 Investigate the effects of loading on beams, columns and struts determine the support reactions, slope and deflection of simply supported beams determine the distribution of stress in the materials of reinforced concrete beams determine the stress distribution in columns and walls which are subjected to asymmetrical bending determine the appropriate critical load for axially loaded struts carry out tests to validate critical load calculations OUTCOME 3 Investigate the behaviour of loaded structural members by considering strain energy determine the strain energy stored in a member due to direct loading, shear loading, bending and torsion determine the elastic deflection of loaded members making appropriate use of Castigliano's theorem carry out tests to validate deflection calculations predict the effects of shock loading on struts and ties

2 MERIT identify and apply strategies to find appropriate solutions. Descriptor effective judgments have been made complex problems with more than one variable have been explored an effective approach to study and research has been applied Achieved select/design and apply appropriate methods/ techniques present and communicate the appropriate findings relevant theories and techniques have been applied. a range of methods and techniques have been applied. a range of sources of information has been used. the selection of methods and techniques/sources has been justified the design of methods/techniques has been justified complex information/data has been synthesized and processed appropriate learning methods/techniques have been applied the appropriate structure and approach has been used coherent, logical development of principles/concepts for intended audience a range of methods of presentation have been used and technical language has been accurately used communication has taken place in familiar and unfamiliar contexts the communication is appropriate for familiar and unfamiliar audiences and appropriate media have been used DISTINCTION use critical reflection to evaluate own work and justify valid conclusions take responsibility for managing and organising activities demonstrate convergent/lateral/ creative thinking conclusions have been arrived at through synthesis of ideas and have been justified the validity of results has been evaluated using defined criteria self-criticism of approach has taken place realistic improvements have been proposed against defined characteristics for success autonomy/independence has been demonstrated substantial activities, projects or investigations have been planned, managed and organised activities have been managed the unforeseen has been accommodated the importance of interdependence has been recognised and achieved ideas have been generated and decisions taken self-evaluation has taken place convergent and lateral thinking have been applied problems have been solved innovation and creative thought have been applied receptiveness to new ideas is evident effective thinking has taken place in unfamiliar contexts

3 Feedback Comments: This Assessment brief has been internally verified by...date... Grade Awarded: Tutor Signature Date:... The script has been internally verified by... Date...

4 PART 1 MOHR'S CIRCLE OF STRESS and FAILURE THEORY INTRODUCTION A certain material is stressed on the x and y planes with an accompanying shear stress. Each student will be given allotted a set of values from the table below. The properties of the material are as follows. E = 205 GPa Poisson's ratio is ν = 0.27 The safe stress level determined in a tensile test is 400 MPa. Draw Mohr's Circle of stress and determine the principal stresses the maximum shear stress and clearly state the position of the principal planes. Using the formula relating 2 dimensional stress and strain, calculate the principal strains using the elastic constants below. Produce a sketch of the element showing the stresses acting on it. Show the principal planes and indicate their relative positions to the x and y planes. Determine the safety factor based on o The greatest principal stress theory. o The greatest principal strain theory. o The maximum shear stress theory. Student Stress on x plane Stress on y plane Shear stress on x MPa MPa MPa

5 DETAILS PART 2 STRAIN GAUGE ROSETTE In order to conduct experimental strain measurement on a structure subject to two stresses, special apparatus is needed. A convenient way to produce a complex stress situation is to pressurise a thin metal cylinder. Commercially available apparatus may be used but any canister designed to hold pressure could be adapted. Care must be taken to ensure safety in the event of rupture. Use only liquid and never gas. Provide a Perspex screen. A 45 o or 60 o strain gauge rosette must be attached to the surface in the prescribed manner. Align the rosette so that no gauge is pointing circumferentially nor longitudinally. Make an accurate measurement of the angles relative to the length. When the cylinder is pressurised, it grows in circumference and length producing tensile stress in both directions. You will need appropriate strain gauge equipment for measuring the strains. Without proof it can be shown that the theoretical stresses may be accurately predicted by the following formulae. The circumferential stress is σ C = pd/2t The longitudinal stress is σ L = pd/4t D is the mean diameter of the cylinder and t is the thickness of the wall. p is the gauge pressure. The formulae for converting principal strains into principal stresses are given below. E E σ1 ε1 νε2 σ 2 2 ε 2 νε1 2 1 ν 1 ν Your task is to measure the strains when the cylinder is pressurised to pressure p and deduce the principal stresses and the directions of the principal planes. You will need to know the value of E (modulus of elasticity) for the material. Attach each strain gauge in turn to a strain measuring instrument following appropriate guide lines. Pump up the pressure to an appropriate level and record the strains on A, B and C. You should repeat it several times and take an average. With the results for each gauge, construct a strain circle and determine the principal strains. Show that the principal strains are longitudinal and circumferential in direction. Convert the principal strains into principal stresses. Compare the principal stresses with those predicted by the formulae.

Name :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CE-NEW)/SEM-3/CE-301/ SOLID MECHANICS

Name :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CE-NEW)/SEM-3/CE-301/ SOLID MECHANICS Name :. Roll No. :..... Invigilator s Signature :.. 2011 SOLID MECHANICS Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are required to give their answers