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    Final Spring 2024

    Uploaded by

    Mohammad Nasreddine

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Final Spring 2024

    Uploaded by

    Mohammad Nasreddine
    8 views4 pages

    Copyright

    © © All Rights Reserved

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    PDF, TXT or read online from Scribd

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    Copyright:

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

    Final Spring 2024

    Uploaded by

    Mohammad Nasreddine

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    You are on page 1of 4

    Problem 1: (30 pts)

    The beam shown in Figure 1 is supported by a pin at 4 and a roller at E. The beam has a
    circular cross-section of radius R. The beam is made from a steel alloy having a yield stress
    σy = 250MPa.

    a) Using the graphical method: Draw the shear force diagram (SFD) and the bending moment
    diagram (BMD) and deduce the maximum bending moment Mmax.

    b) Using a safety factor against failure by yielding = 2, determine the required radius R of the
    cross-section.
    Problem 2: (20 pts)

    The beam shown in Figure 2 is suuported by a pin at A and roller at C and subjected to linear
    istributed loading between A and B and constant distributed loading between B and C.

    Find the equations of shear force V and bending moment M along the beam for

    0 ≤ x ≤ 1.5m and 0 ≤ x ≤ 2m.


    Problem 3: (30 pts)

    gure 3 shows the cross-sectional area of a beam subjected to a maximum shear force V-SKN.
    he beam is made from a material having an allowable shear stress Tallow=40MPa.

    a) Locate the centroid C of the cross-section and calculate the moment of inertia I/N.A of the
    cross-section about the neutral axis in terms of t.

    b) Caclulate the maximum shear stress ta in terms of and deduce the required thickness of the
    cross-section in order to avoid failure due to shear,

    c) For t = 10 mm, calculate the shear stresses at points: B, B’ , C and and plot the shear stress
    distribution along the cross-section.
    Problem 4: (20pts)

    A stepped shaft shown in Figure 4 consisting of two solid circular segments subjected to
    torques T1 = 2kN.m and T2 = 0.8kN.m. The segment AB has a diameter di 60 mm and length
    L = 0.8m, while the segment BC has a diameter dy = 40 mm and length L2 0.6m.

    The shaft is made from a steel alloy having a shear modulus G = 77 GPa and a yield shear
    strength Ty=150 MPa.

    a) Draw the diagram of internal torque along the shaft

    b) Calculate the absolute maximum shear in the shaft and deduce the safety factor against
    vielding

    c) Calculate the angle of twist at the right end C of the shaft.

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