Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
5th Edition
ISBN: 9780073398006
Author: Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher: McGraw-Hill Education
Question
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Chapter 11, Problem 1P
To determine

Find the reactions and plot the shear force and bending moment diagrams.

Mention the points of inflection and mention the maximum shear and moment in each span.

Expert Solution & Answer
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Explanation of Solution

Given information:

EI is constant.

Calculation:

Find the stiffness of each member connected to joint B as follows;

KBA=ILBA=I24KBC=ILBC=I12

Find the total stiffness at joint B as follows;

KB=KBA+KBC=I24+I12=I8

Find the distribution factors at joint B using the relation;

DFBA=KBAKB=I24I8=13

DFBC=KBCKB=I12I8=23

Refer the appendix Table A.4 to find the fixed end moments.

Find the fixed end moment at each end of the member AB as follows;

FEMAB=PLAB8=30×248=90kips-ft

FEMBA=+PLBA8=+30×248=+90kips-ft

Find the fixed end moment at each end of the member BC as follows;

FEMBC=wLBC212=3.5×12212=42kips-ft

FEMCB=+wLCB212=+3.5×12212=+42kips-ft

Show the moment distribution computations as in Figure 1.

Fundamentals of Structural Analysis, Chapter 11, Problem 1P , additional homework tip  1

Show the members AB and BC as in Figure 2.

Fundamentals of Structural Analysis, Chapter 11, Problem 1P , additional homework tip  2

Refer Figure (2),

Consider member AB:

Take moment about point A;

MA=0VBA(24)7430(12)+98=024VBA+24360=0VBA=14kips()

Resolve the vertical component of forces.

Fy=0VAB30+VBA=0VAB30+14=0VAB=16kips()

Consider member BC:

Take moment about point B;

MB=0VCB(12)263.5(12)(122)+74=012VCB+48252=0VCB=17kips()

Resolve the vertical component of forces.

Fy=0VBC3.5(12)+VCB=0VBC42+17=0VBC=25kips()

Show the free body diagram of the shear force and bending moment as in Figure 3.

Fundamentals of Structural Analysis, Chapter 11, Problem 1P , additional homework tip  3

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