Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
9th Edition
ISBN: 9781337594318
Author: Barry J. Goodno; James M. Gere
Publisher: Cengage Learning
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Chapter 10, Problem 10.3.1P

A propped cantilever steel beam is constructed from a W12 × 35 section. The beam is loaded by its self-weight with intensity q. The length of the beam is 1L5 ft. Let E = 30,000 ksi.

  1. Calculate the reactions at joints A and B.

  • Find the location of zero moment within span AB.
  • Calculate the maximum deflection of the beam and the rotation at joint B.
  •   Chapter 10, Problem 10.3.1P, A propped cantilever steel beam is constructed from a W12 × 35 section. The beam is loaded by its

    a.

    Expert Solution
    Check Mark
    To determine

    The reaction at joint A and B.

    Answer to Problem 10.3.1P

      RB=0.151kipsRA=0.252kipsMA=0.57kipf

    Explanation of Solution

    Given information:

      Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card, Chapter 10, Problem 10.3.1P

      for W12×35,q=35 {(from appendix f(a)}L=11.5ftE=30000ksi

    The first step is to consider the equilibrium condition of the entire beam, express the other two reaction in term of RB .

    We have,

      RA=qLRB,MA=qL22RBL

    Bending moment,

    Consider a distance x away from the fixed support.

      M=RAxMAqx22

    On substituting the values,

      M=qLxRBxqL22+RBLqx22

    The second order of differential equation of deflection curve becomes,

      Elv=M=qLxRBxqL22+RBLqx22

    On two successive integrations, we obtain the equation of slope and deflection:

    Slope:

      Elv=qLx22RBx22qL2x2+RBLxqx36+c1

    Deflection:

      Elv=qLx36RBx36qL2x24+RBLx22qx424+c1x+c2

    These equations contain three unknown quantities:

      (c1,c2,RB)

    Applying boundary conditions,

      v(0)=0c1=0v(0)=0c2=0

      RB=3qL8=0.151kipsRA=5qL8=0.252kipsMA=qL22RBL=0.57kipft

    b.

    Expert Solution
    Check Mark
    To determine

    The location of zero moment within span AB.

    Answer to Problem 10.3.1P

      xzero=2.875ft

    Explanation of Solution

    X zero means, the position at which the value of bending moment is zero.

    The bending moment is zero at:

      xzero=L4xzero=11.54=2.875ft

    c.

    Expert Solution
    Check Mark
    To determine

    The maximum deflection of beam and the rotation at joint B.

    Answer to Problem 10.3.1P

      δmax=6.67×104in

      θB=1.86×105rad

    Explanation of Solution

    Given information:

      {(from appendix f(a)}q=35lbI=285in4L=11.5ftE=30000ksi

    Maximum deflection:

      δmax=qx24LEI=6.67×104in

    Rotation at joint B,

      θB=qL324EI

      θB=1.86×105rad

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    Chapter 10 Solutions

    Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card

    Ch. 10 - A fixed-end b earn of a length L is loaded by a...Ch. 10 - A fixed-end beam of a length L is loaded by...Ch. 10 - A counterclockwise moment M0acts at the midpoint...Ch. 10 - A propped cantilever beam of a length L is loaded...Ch. 10 - A propped cantilever beam is subjected to uniform...Ch. 10 - Repeat Problem 10.3-15 using L = 3.5 m, max = 3...Ch. 10 - A two-span, continuous wood girder (E = 1700 ksi)...Ch. 10 - A fixed-end beam AB carries point load P acting at...Ch. 10 - A fixed-end beam AB supports a uniform load of...Ch. 10 - -4-4 A cantilever beam is supported at B by cable...Ch. 10 - A propped cantilever beam AB of a length L carries...Ch. 10 - A beam with a sliding support at B is loaded by a...Ch. 10 - A propped cantilever beam of a length 2L with a...Ch. 10 - The continuous frame ABC has a pin support at /l,...Ch. 10 - The continuous frame ABC has a pin support at A,...Ch. 10 - Beam AB has a pin support at A and a roller...Ch. 10 - The continuous frame ABCD has a pin support at B:...Ch. 10 - Two flat beams AB and CD, lying in horizontal...Ch. 10 - -4-13 A propped cantilever beam of a length 2L is...Ch. 10 - A propped cantilever beam of a length 2L is loaded...Ch. 10 - Determine the fixed-end moments (MAand MB) and...Ch. 10 - A continuous beam ABC wit h two unequal spans, one...Ch. 10 - Beam ABC is fixed at support A and rests (at point...Ch. 10 - A propped cantilever beam has flexural rigidity EI...Ch. 10 - A triangularly distributed 1oad with a maximum...Ch. 10 - A fixed-end beam is loaded by a uniform load q =...Ch. 10 - Uniform load q = 10 lb/ft acts over part of the...Ch. 10 - A propped cantilever beam with a length L = 4 m is...Ch. 10 - A cant i levé r b ea m i s supported by a tie rod...Ch. 10 - The figure shows a nonprismatic, propped...Ch. 10 - A beam ABC is fixed at end A and supported by beam...Ch. 10 - A three-span continuous beam A BCD with three...Ch. 10 - A beam rests on supports at A and B and is loaded...Ch. 10 - A propped cantilever beam is subjected to two...Ch. 10 - A propped cantilever beam is loaded by a...Ch. 10 - A fixed-end beam AB of a length L is subjected to...Ch. 10 - A temporary wood flume serving as a channel for...Ch. 10 - Two identical, simply supported beams AB and CD...Ch. 10 - The cantilever beam AB shown in the figure is an...Ch. 10 - The beam AB shown in the figure is simply...Ch. 10 - The continuous frame ABC has a fixed support at A,...Ch. 10 - The continuous frame ABC has a pinned support at...Ch. 10 - A wide-flange beam ABC rests on three identical...Ch. 10 - A fixed-end beam AB of a length L is subjected to...Ch. 10 - A beam supporting a uniform load of intensity q...Ch. 10 - A thin steel beam AB used in conjunction with an...Ch. 10 - Find an expression for required moment MA(in terms...Ch. 10 - Repeat Problem 10.4-41 for the loading shown in...Ch. 10 - A propped cantilever beam is loaded by two...Ch. 10 - A cable CD of a length H is attached to the third...Ch. 10 - A propped cantilever beam, fixed at the left-hand...Ch. 10 - Solve t he preceding problem by integrating the...Ch. 10 - A two-span beam with spans of lengths L and L/3 is...Ch. 10 - Solve the preceding problem by integrating the...Ch. 10 - Assume that the deflected shape of a beam AB with...Ch. 10 - (a) A simple beam AB with length L and height h...
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