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    Homework 1

    Uploaded by

    Mack Bragais Bon
    This document contains 6 mechanics of materials homework problems related to stresses and forces in structural elements like trusses, bolts, pins, and beams. Problem 1 involves calculating bearing stress on a pin connecting truss members. Problem 2 looks at shear and bearing stresses in a bicycle brake pivot pin. Problem 3 calculates tensile force and shear stress in a bicycle chain. Problem 4 determines the maximum torque transmittable by bolts. Problem 5 involves shear stress and bolt diameter for a load carried by an inclined strut and beam. Problem 6 calculates allowable load on a truss based on stresses in angles, rivets, and gusset plate.

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    Homework 1

    Uploaded by

    Mack Bragais Bon
    202 views2 pages
    This document contains 6 mechanics of materials homework problems related to stresses and forces in structural elements like trusses, bolts, pins, and beams. Problem 1 involves calculating bearing stress on a pin connecting truss members. Problem 2 looks at shear and bearing stresses in a bicycle brake pivot pin. Problem 3 calculates tensile force and shear stress in a bicycle chain. Problem 4 determines the maximum torque transmittable by bolts. Problem 5 involves shear stress and bolt diameter for a load carried by an inclined strut and beam. Problem 6 calculates allowable load on a truss based on stresses in angles, rivets, and gusset plate.

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    This document contains 6 mechanics of materials homework problems related to stresses and forces in structural elements like trusses, bolts, pins, and beams. Problem 1 involves calculating bearing stress on a pin connecting truss members. Problem 2 looks at shear and bearing stresses in a bicycle brake pivot pin. Problem 3 calculates tensile force and shear stress in a bicycle chain. Problem 4 determines the maximum torque transmittable by bolts. Problem 5 involves shear stress and bolt diameter for a load carried by an inclined strut and beam. Problem 6 calculates allowable load on a truss based on stresses in angles, rivets, and gusset plate.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    202 views2 pages

    Homework 1

    Uploaded by

    Mack Bragais Bon
    This document contains 6 mechanics of materials homework problems related to stresses and forces in structural elements like trusses, bolts, pins, and beams. Problem 1 involves calculating bearing stress on a pin connecting truss members. Problem 2 looks at shear and bearing stresses in a bicycle brake pivot pin. Problem 3 calculates tensile force and shear stress in a bicycle chain. Problem 4 determines the maximum torque transmittable by bolts. Problem 5 involves shear stress and bolt diameter for a load carried by an inclined strut and beam. Problem 6 calculates allowable load on a truss based on stresses in angles, rivets, and gusset plate.

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    Mechanics of Materials I

    Homework assignment # 1

    Problem 1. Truss members supporting a roof are


    connected to a 26-mm-thick gusset plate by a 22 mm
    diameter pin as shown in the figure and photo. The two
    end plates on the truss members are each 14 mm thick.
    (a) If the load P = 80 kN, what is the largest bearing
    stress acting on the pin?
    (b) If the ultimate shear stress for the pin is 190 MPa,
    what force P is required to cause the pin to fail in
    shear?
    (Disregard friction between the plates.)

    Problem 2. The force in the brake cable of the V-brake


    system shown in the figure is T = 45 lb. The pivot pin at
    A has diameter d 0.25 in and length L 5/8 in.
    Use dimensions shown in the figure. Neglect the weight
    of the brake system.
    (a) Find the average shear stress τ in the pivot pin
    where it is anchored to the bicycle frame at B.
    (b) Find the average bearing stress σ , in the pivot
    pin over
    segment AB.

    Problem 3. A bicycle chain consists of a series of small


    links, each 12 mm long between the centers of the pins
    (see figure). You might wish to examine a bicycle chain
    and observe its construction. Note particularly the pins,
    which we will assume to have a diameter of 2.5 mm. In
    order to solve this problem, you must now make two
    measurements on a bicycle (see figure): (1) the length L
    of the crank arm from main axle to pedal axle, and (2)
    the radius R of the sprocket (the toothed wheel,
    sometimes called the chainring). Suppose L=162 mm
    and R=90 mm.
    (a) Calculate the tensile force T in the chain due to a
    force F=800 N applied to one of the pedals.
    (b) Calculate the average shear stress τ in the pins.
    Problem 4. A torque T is transmitted between two
    flanged shafts by means of ten 20-mm bolts (see figure
    and photo). The diameter of the bolt circle is d=250 mm.
    If the allowable shear stress in the bolts is 90 MPa, what
    is the maximum permissible torque?
    (Disregard friction between the flanges.)

    Problem 5. A horizontal beam AB with cross-sectional


    dimensions (b=0.75 in) and (h=8.0 in.) is supported by
    an inclined strut CD and carries a load P=2700 lb at
    joint B [see figure part (a)]. The strut, which consists of
    two bars each of thickness 5b/8, is connected to the
    beam by a bolt passing through the three bars meeting at
    joint C [see figure part (b)].
    (a) If the allowable shear stress in the bolt is 13,000 psi,
    what is the minimum required diameter d of the bolt
    at C?
    (b) If the allowable bearing stress in the bolt is 19,000
    psi, what is the minimum required diameter d of the
    bolt at C?

    Problem 6. A plane truss is subjected to loads 2P and P at joints B and C, respectively, as shown in the figure part
    (a). The truss bars are made of two steel angles [cross sectional area of the two angles, A 2180 mm , figure part
    (b)] having an ultimate stress in tension equal to 390 MPa. The angles are connected to a 12 mm-thick gusset plate
    at C [figure part (c)] with 16-mm diameter rivets; assume each rivet transfers an equal share of the member force to
    the gusset plate. The ultimate stresses in shear and bearing for the rivet steel are 190 MPa and 550 MPa,
    respectively.
    Determine the allowable load P if a safety factor of 2.5 is desired with respect to the ultimate load that can be
    carried.
    (Consider tension in the bars, shear in the rivets, bearing between the rivets and the bars, and also bearing between
    the rivets and the gusset plate. Disregard friction between the plates and the weight of the truss itself.)

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