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    Mech Sol - 2020 - Compre Part A&b

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    rohit Bind
    The document is a comprehensive examination for a Mechanics of Solids course consisting of 4 questions with multiple parts each. Question 1 involves calculating bending moment diagrams and minimum diameter for a bracket. Question 2 uses Mohr's circle to find stresses from principal strains. Question 3 determines reactions, deflection, and strain energy in a curved beam. Question 4 evaluates factors of safety using two failure criteria for a state of plane stress in a machine component. The examination also includes 4 open book questions involving buckling of columns, stresses in a box beam, deflection of a loaded beam, and torques required to produce a specified twist in connected shafts.

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    Mech Sol - 2020 - Compre Part A&b

    Uploaded by

    rohit Bind
    17 views4 pages
    The document is a comprehensive examination for a Mechanics of Solids course consisting of 4 questions with multiple parts each. Question 1 involves calculating bending moment diagrams and minimum diameter for a bracket. Question 2 uses Mohr's circle to find stresses from principal strains. Question 3 determines reactions, deflection, and strain energy in a curved beam. Question 4 evaluates factors of safety using two failure criteria for a state of plane stress in a machine component. The examination also includes 4 open book questions involving buckling of columns, stresses in a box beam, deflection of a loaded beam, and torques required to produce a specified twist in connected shafts.

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    Mech Sol_2020_Compre Part a&B

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    The document is a comprehensive examination for a Mechanics of Solids course consisting of 4 questions with multiple parts each. Question 1 involves calculating bending moment diagrams and minimum diameter for a bracket. Question 2 uses Mohr's circle to find stresses from principal strains. Question 3 determines reactions, deflection, and strain energy in a curved beam. Question 4 evaluates factors of safety using two failure criteria for a state of plane stress in a machine component. The examination also includes 4 open book questions involving buckling of columns, stresses in a box beam, deflection of a loaded beam, and torques required to produce a specified twist in connected shafts.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    17 views4 pages

    Mech Sol - 2020 - Compre Part A&b

    Uploaded by

    rohit Bind
    The document is a comprehensive examination for a Mechanics of Solids course consisting of 4 questions with multiple parts each. Question 1 involves calculating bending moment diagrams and minimum diameter for a bracket. Question 2 uses Mohr's circle to find stresses from principal strains. Question 3 determines reactions, deflection, and strain energy in a curved beam. Question 4 evaluates factors of safety using two failure criteria for a state of plane stress in a machine component. The examination also includes 4 open book questions involving buckling of columns, stresses in a box beam, deflection of a loaded beam, and torques required to produce a specified twist in connected shafts.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 4

    BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI

    First Semester 2019-2020


    ME/ MF F211: Mechanics of Solids
    Comprehensive Regular Examination
    Date: 6.12.19 Time: 1 Hr Max Marks: 30

    Note: (1) There are total 4 questions


    (2) Both side of the paper is printed.
    (3) The time allotted is 1 hr for Part-A but you can take time as per your convenience. After
    submitting Part- A, you can take the question paper and answer sheet for Part- B.
    ___________________________________________________________________________
    PART-A(CLOSED BOOK)

    Q1. Bracket ABCD of solid circular cross-section has the shape and dimension (b = 37mm) as
    shown in FigQ1. A vertical and horizontal load P (40 N) acts at the free end D.
    (a) Draw the bending moment diagram of bracket ABCD. Hint: Show the variation of
    bending moment along segments AB, BC and CD separately.
    (b) Determine the minimum permissible diameter dmin of the bracket, if the allowable
    bending stress in the material is 30 MPa. (Neglect the weight of bracket) [8]

    Fig Q1

    Q2. The principal strains in the plane of a flat aluminum plate loaded in its plane are
     1  8.1  10 4  2  5.7  10 4 . Using Mohr’s circle, find x, y, and xy where the x and y
    axes are as shown in FigQ2. Take E = 72GPa and  = 0.33. [7]

    Fig Q2
    Q3. The curved cantilever beam in FigQ3 has a radius of curvature R and a circular cross
    section of diameter d. It is subjected to a point load P at point B.
    (a) Determine the reactions (i.e. axial force, shear force and bending moment) acting at any
    section θ in the curved cantilever beam AB.
    (b) Using Castigliano’s method (the strain energy method), determine the vertical
    deflection of point B in terms of P, modulus of elasticity E, radius of curvature R, cross-
    section area A, and moment of inertia of the cross section I. Neglect the effect of strain
    energy due to shear [8]

    Fig Q3

    Q4. The state of plane stress shown (in FigQ4) occurs at a critical point of a steel machine
    components. As a result of several tensile tests, it has been found that the tensile yield
    strength is Y = 270 MPa for the grade of steel used. Determine the factor of safety with
    respect to yield, using
    (a) maximum-shearing-stress (MSS) criterion and (b) Distortion energy criterion [7]

    Fig Q4
    BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
    First Semester 2019-2020
    ME F211/MF F211: Mechanics of Solids
    Comprehensive Examination
    Date: 6.12.19 Time: 2 Hr Max Marks: 50

    PART-B (OPEN BOOK)

    Q1. In Fig Q1, member OA can be considered rigid and weightless. Column BC is pin-ended and
    column DF is pin-ended at A and fixed at F. Both the columns are of solid circular cross-sections
    of diameter 10mm. Column BC is made of structural steel (E = 200GPa) and column DF is made
    of an Aluminium alloy (E = 72GPa). Determine the magnitude of Q that will cause one of the
    columns to buckle. [10]

    Q2.The box beam is subjected to the 26 kN inclined force (as shown in FigQ2) that is applied at the
    center of its width, 75 mm from each side.
    a. Calculate the axial force F, shear force V, and bending moment Mb acting on the cross
    section x-x.
    b. Determine the stress components (i.e.  x and  xy ) on elements at points A and B.
    c. Show these stresses on properly oriented 2-D elements.
    d. Determine the principal stresses (i.e.  1 and  2 ) at point A. [18]

    Section x-x:

    Fig Q2
    Q3.The beam AB in FigQ3 is fixed supported to the wall at A and pin connected to a 12 mm
    diameter rod BC at B. The beam is subjected to a point load P = 40 kN at D as shown in Fig. If
    E = 210 GPa for both the members (i.e. beam AB and rod BC),
    a) Determine the force developed in the rod BC due to the loading.
    b) State the proper boundary conditions and starting from the fourth-order differential equation
    (i.e. the load equation), derive the equation of deflection curve for the beam AB.
    c) Determine the deflection of point B on the beam.
    The moment of inertia of the beam about its neutral axis is INA= 186 x 106 mm4. [10]

    Fig Q3

    Q4. The 60-mm diameter shaft ABC is supported by two journal bearings, while the 80-mm
    diameter shaft EH is fixed at E and supported by a journal bearing at H (FigQ4). If the
    angle of twist at gears A and C is required to be 0.05 rad, determine the magnitudes of the
    torques T1 and T2. The shafts are made of A-36steel (G = 80 GPa). [12]

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