Structural Mechanics MOD009161 Exam Information

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Questions and Answers

Match the following beam loading conditions with the correct formula for maximum deflection:

Simply supported beam, concentrated load at mid-span = $\frac{PL^3}{48EI}$ Simply supported beam, uniformly distributed load = $\frac{5wL^4}{384EI}$ Cantilever beam, concentrated load at free end = $\frac{PL^3}{3EI}$ Cantilever beam, uniformly distributed load = $\frac{wL^4}{8EI}$

Match the following terms related to beam analysis with their definitions:

Shear Force = Internal force acting perpendicular to the cross-section of the beam. Bending Moment = Internal moment acting about the neutral axis of the beam. Neutral Axis = Axis within the beam cross-section where there is no bending stress. Deflection = The displacement of a beam from its original position under load.

Match the following beam support types with their corresponding reaction characteristics:

Hinged Support = Resists vertical and horizontal forces, but not moments. Roller Support = Resists force perpendicular to the surface, but not parallel forces or moments. Fixed Support = Resists vertical and horizontal forces and moments. Free End = No resistance to forces or moments.

Match the cross-sectional properties of a beam with their significance in structural analysis:

<p>Area = Influences axial stress capacity. Second Moment of Area = Influences bending stiffness and resistance to deflection. Section Modulus = Influences bending stress capacity. Radius of Gyration = Related to buckling resistance of columns.</p> Signup and view all the answers

Match each concept with its appropriate formula related to stress and strain:

<p>Bending Stress = $σ = \frac{My}{I}$ Axial Stress = $σ = \frac{N}{A}$ Shear Stress = $τ = \frac{V}{A}$ Strain = $ε = \frac{ΔL}{L}$</p> Signup and view all the answers

Match the following materials with their typical values in structural engineering:

<p>Steel = High strength and stiffness, prone to corrosion if not treated. Concrete = High compressive strength, low tensile strength, brittle. Timber = Good strength-to-weight ratio, susceptible to moisture and decay. Aluminum = Lightweight, corrosion-resistant, lower stiffness than steel.</p> Signup and view all the answers

Match the following structural analysis methods with their suitable applications:

<p>Direct Stiffness Method = Analyzing complex structures with many degrees of freedom. Method of Sections = Finding internal forces in specific members of a truss. Virtual Work Method = Determining deflections in beams and trusses. Influence Lines = Determining the effect of moving loads on internal forces and reactions.</p> Signup and view all the answers

Match the following failure modes with their descriptions:

<p>Yielding = Permanent deformation of a material after exceeding its yield strength. Buckling = Sudden lateral instability of a slender compression member. Fracture = Separation of a material due to exceeding its ultimate tensile strength. Fatigue = Failure due to repeated cyclic loading, even below the yield strength.</p> Signup and view all the answers

Match the following concepts relevant to column design with their descriptions:

<p>Euler Buckling Load = Theoretical critical load for a perfectly straight column. Effective Length = Length of an equivalent pinned-end column with the same buckling load. Slenderness Ratio = Ratio of effective length to the least radius of gyration. Critical Stress = Stress at which a column buckles.</p> Signup and view all the answers

Match each term related to section properties with its definition:

<p>Centroid = The geometric center of a cross-section. Moment of Inertia = A measure of a cross-section's resistance to bending. Radius of Gyration = A measure of a cross-section's resistance to buckling. Section Modulus = A measure of a cross-section's resistance to bending stress.</p> Signup and view all the answers

Match the following aspects of structural design with considerations relevant to them:

<p>Safety = Factors of safety, load combinations, and material properties. Serviceability = Deflections, vibrations, and cracking. Durability = Corrosion resistance, material degradation, and environmental effects. Sustainability = Life-cycle assessment, embodied energy, and recyclability.</p> Signup and view all the answers

Match the following types of loads acting on structures with their characteristics:

<p>Dead Load = Permanent loads due to the weight of structural elements and fixed equipment. Live Load = Variable loads due to occupancy, furniture, and movable equipment. Wind Load = Lateral loads caused by wind pressure or suction. Seismic Load = Dynamic loads induced by earthquake ground motion.</p> Signup and view all the answers

Match the following dimensionless numbers with their representation:

<p>Poisson’s Ratio = Ratio of transverse strain to axial strain. Bulk Modulus = Measure of a substance's resistance to uniform compression. Young's Modulus = Measure of a solid's stiffness or resistance to elastic deformation under stress. Shear Modulus = Measure of a solid's resistance to shear stress.</p> Signup and view all the answers

Match the following common structural member with the force they largely resist:

<p>Beams = Bending moments and shear forces. Columns = Compressive axial loads. Cables = Tensile forces. Shear walls = Lateral loads.</p> Signup and view all the answers

Match the following common truss elements with their descriptions:

<p>Top Chord = The top-most horizontal member. Bottom Chord = The bottom-most horizontal member. Web Members = The diagonal and vertical members connecting the chords. Joints = The connection points where truss members are connected.</p> Signup and view all the answers

Flashcards

Structural Mechanics

Structural mechanics is the study of the behavior of structures under loads.

Free Body Diagram (FBD)

A diagram representing forces and moments acting on a body.

Shear Force

Internal force acting parallel to the cross-section of a material.

Normal Force

Internal force acting perpendicular to the cross-section of a material.

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Bending Moment

Internal moment that resists bending due to applied loads.

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Uniformly Distributed Load (UDL)

A load that is distributed evenly over the length of a structural element.

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Stiffness

The resistance of a structural member to deformation.

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Yield Stress

The stress at which a material begins to deform permanently

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Steel Grade S355

A standard for steel materials, indicating specific mechanical properties.

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Modulus of Elasticity

A measure of a material's resistance to elastic deformation under stress.

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Bending Stress

A type of stress caused by a bending moment in a structural member.

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Centroid

The point where the area of a shape is equally distributed around it.

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Bending Moment

The bending moment in a structural member is the reaction induced in that member when an external force or moment is applied to the member causing the member to bend.

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Second Moment of Area

A measure of beam's resistance to bending.

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Study Notes

  • The exam period is July/August 2024
  • The faculty is Science and Engineering
  • The discipline is Mechanical Engineering
  • The module code is MOD009161
  • The module title is Structural Mechanics
  • The level is level 4, with 15 credits
  • The exam duration is 2 hours
  • The exam will have 3 questions in Part A and 3 questions in Part B
  • There are 12 pages including the cover page
  • The name of the tutor is Dr Shadi Ostovari
  • Books, statutes, case studies, and formulae tables are not allowed unless they are provided by the university.
  • Students are not allowed to bring their own books, statutes, or case studies
  • Graph paper is not allowed
  • Only standard scientific, non-programmable calculators are allowed
  • No other stationery or materials are permitted
  • The exam is in two parts and totals 100 marks
  • Answer all three questions in Part A, with each question carrying different marks
  • Answer any TWO questions in Part B; each question is worth 20 marks. No marks will be awarded for an extra Part B question
  • Electronic equipment capable of displaying textual information, including mobile phones and smart watches, must be left at the front of the examination room
  • Formula sheets are provided at the end of the question sheets
  • Start each question on a new page in your answer booklet
  • Show all calculations, clearly state all assumptions and units
  • Use diagrams and sketches to explain answers where needed
  • Manage time effectively, allocating it based on available marks
  • Read each question carefully before answering
  • The exam paper must not be removed from the exam hall

Part A

  • Attempt all three questions
  • Question one concerns a barn that has a beam that spans between the side walls
  • The beam has a length of 6m
  • The beam has two struts that transfer loads down from the roof onto it at the third points
  • You must produce a diagram to represent this beam and the actions, and what you would consider when carrying out analysis in order to determine the design bending moment and shear force
  • You must sketch the shape of the bending moment and shear force diagrams you would expect to get from analysing your model(s)
  • No numerical value is needed on the bending moment and shear force diagrams
  • Use P for the point loads and w for a Uniformly distributed load
  • Question two concerns three cross-sections in Figure QA2.1 which belong to three simply supported beams with a span of 6 m
  • Beams are made of steel plates S355, each with the same amount of material
  • For example: they are made of three 15mm thick by 200 mm wide plates
  • The three steel beams are simply supported with a span of 6 m and carry a Uniformly Distributed Load (UDL) of 40 KN/m
  • Advantages of steel beams being I-shaped and not rectangular must be explained in terms of their geometric properties
  • Find the second moment of area of each cross-section and comment on the stiffness of each beam
  • You must then explain which beam will produce the lowest deflection under a UDL of 40 KN/m and then find the value of the lowest deflection
  • You must draw the bending moment and shear force diagrams for the beam under a UDL of 40 KN/m
  • You must explain which beam produces the lowest bending stress using the bending stress equation
  • Find the value of the stress for each beam under UDL of 40 KN/m
  • Consider the yield stress of fy = 355 MPa, for the steel of grade S355, and then comment on the suitability of each beam under the given load using the permissible stress design philosophy
  • The density of steel is 7850 kg/m³
  • The modulus of elasticity is E = 210000 MPa
  • Question three concerns the beam shown in Figure QA3.1 which is designed to carry a load of 25KN/m
  • The beam is simplified to an equivalten load of 200KN applied at the centre of the beam
  • You must draw the bending moment diagram for both beams and comment on the accuracy of the method adopted by the graduate engineer for finding the maximum bending moment

Part B

  • Attempt two of the three questions
  • Question one requires the position of the centroid of a cross-section of a beam to be determined, as shown in Figure QB.1
  • Calculate the second moment of area about the x' – x' axis through its centroid
  • Question two, uses Figure QB.2, which shows a simply supported beam under the actions of a point load and one uniformly distributed load (UDL)
  • You must calculate all the reactions in beam supports A and B
  • You must calculate the shear forces, as well as draw the shear force diagram of the beam under the actions
  • You must calculate the bending moments, as well as draw the bending moment diagram of the beam under the actions
  • The maximum values of both shear force and bending moment are to be determined
  • Question three refers to a box connected to point D which is a weight of 550 N (Figure QB.3)
  • A suitable Free Body Diagram (FBD) must be drawn for finding the force in each cable
  • You must find the force in each supporting cable

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