   Chapter 10, Problem 10.4.8P ### Mechanics of Materials (MindTap Co...

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

#### Solutions

Chapter
Section ### 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. 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.

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