BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
Textbook Problem

The continuous frame ABC has a pin support at /l, roller supports at B and C, and a rigid corner connection at B (see figure). Members AB and BC each have flexural rigidity EI. A moment M0acts counterclockwise at B, Note: Disregard axial deformations in member AB and consider only the effects of bending.

  1. Find all reactions of the frame.

  • Find joint rotations B at A, B, and C.
  • Find the required new length of member BC in terms of L., so that θ B

  • in part (b) is doubled in size.
  •   

    (a)

    To determine

    All the reactions of the frame.

    Explanation

    Given Information:

    The following figure is given with all relevant information,

    Calculation:

    Consider the following free body diagram,

    Take equilibrium of horizontal forces as,

    FH=0HARC=0                       ....(1)

    Take equilibrium of vertical forces as,

    FV=0RA+RB=0                       ....(2)

    Take equilibrium of moments about B as,

    MB=0RAL+M0+RCL/2=0                       ....(3)

    The bending moment at distance x from A along AB in part AB is given by,

    MAB=RAx

    Use second order deflection differential equation,

    d2vdx2=MEI=M ABEId2vdx2=1EI(RAx)                        

    Integrate above equation to get rotation as,

    dvdx=θAB=1EI(RAx2/2+C1)                          

    Integrate above equation to get rotation as,

    v=δAB=1EI(RAx3/6+C1x+C2)            

    The bending moment at distance x from B along BC in part BC is given by,

    MBC=RCL/2RCx

    Use second order deflection differential equation,

      d2vdx2=MEI=M BCEI!

    (b)

    To determine

    Rotations at joints A, B and C.

    (c)

    To determine

    Length of BC.

    Still sussing out bartleby?

    Check out a sample textbook solution.

    See a sample solution

    The Solution to Your Study Problems

    Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

    Get Started

    Additional Engineering Solutions

    Find more solutions based on key concepts

    Show solutions add

    How does a secured bond differ from an unsecured bond?

    Cornerstones of Financial Accounting

    What was the earliest reason for the use of cryptography?

    Principles of Information Security (MindTap Course List)

    Cobalt-chromium alloys, stainless steel, and titanium alloys are three common biomaterials that have been used ...

    Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

    What is an effective way to assess user requests for additional features and functions?

    Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

    ERP a. processing system in which the computer processes each transaction as it is entered b. application of hu...

    Enhanced Discovering Computers 2017 (Shelly Cashman Series) (MindTap Course List)

    Use LRFD and design the hearing stiffeners for the girder of Problem 10.7-4. Use Fy=50 ksi.

    Steel Design (Activate Learning with these NEW titles from Engineering!)