FUNDAMENTALS OF STRUCTURAL ANALYSIS
FUNDAMENTALS OF STRUCTURAL ANALYSIS
5th Edition
ISBN: 9781260170276
Author: Leet
Publisher: MCG
Question
Chapter 13, Problem 1P
To determine

Find the moment at the support B of the beam using approximate analysis.

Sketch the shear and moment diagrams of the beam.

Expert Solution & Answer
Check Mark

Answer to Problem 1P

The moment at the support B of the beam using approximate analysis is 360kipft_.

Explanation of Solution

Given information:

The value of EI is constant.

Apply the sign conventions for calculating reactions, forces and moments using the three equations of equilibrium as shown below.

  • For summation of forces along x-direction is equal to zero (Fx=0), consider the forces acting towards right side as positive (+) and the forces acting towards left side as negative ().
  • For summation of forces along y-direction is equal to zero (Fy=0), consider the upward force as positive (+) and the downward force as negative ().
  • For summation of moment about a point is equal to zero (Matapoint=0), consider the clockwise moment as negative and the counter clockwise moment as positive.

Calculation:

Let consider the location of a point of inflection at 0.25L to the left of support B which means 6 ft to the left of support B or 18 ft from the support A to the right.

Show the location of a point of inflection as in Figure 1.

FUNDAMENTALS OF STRUCTURAL ANALYSIS, Chapter 13, Problem 1P , additional homework tip  1

Find the reaction RA at support A:

Summation of moments about P.I. is equal to 0.

MP.I=0RA(18)5(18)(182)=0RA=45kips

Let RB and RC be the reactions at the supports B and C.

Summation of moments about C is equal to 0.

MC=0RA(44)+RB(20)5(44)(442)=045(44)+RB(20)5(44)(442)=0RB=143kips

Summation of forces along y-direction is equal to 0.

+Fy=0RA+RB+RC5(44)=045+143+RC5(44)=0RC=32kips

Find the shear values of the beam:

FA=45kips

FB,JL=455(24)=75kips

FB,JR=455(24)+143=68kips

FC=32kips

Find the point of zero shear force for span AB,

Fxx=0455x=0x=9ftfrompointA

For span BC,

Fxx=0325x=0x=6.4ftfrompointC

Find the moment values of the beam:

MA=0

MB=45(24)5(24)(242)=360kipft

MC=0

Mx=9ftfrompointA=45(9)5(9)(92)=202.5kipft

Mx=6.4ftfrompointC=32(6.4)5(6.4)(6.42)=102.4kipft

Sketch the shear and moment diagram of the beam using approximate analysis as shown in Figure 2.

FUNDAMENTALS OF STRUCTURAL ANALYSIS, Chapter 13, Problem 1P , additional homework tip  2

Check the shear and moment values using moment distribution method:

Find the fixed end moments in the span AB and BC:

FEMAB=wL212=5(24)212=240kipft

FEMBA=FEMAB=240kipft

FEMBC=wL212=5(20)212=166.7kipft

FEMCB=FEMBC=166.7kipft

Find the distribution factor at joint B:

DFBA=2044=511

DFBC=2444=611

Show the moment distribution table as in Figure 3.

FUNDAMENTALS OF STRUCTURAL ANALYSIS, Chapter 13, Problem 1P , additional homework tip  3

Consider span AB, find the reactions at the supports:

Summation of moments about B is equal to 0.

MB=0RA(24)5(24)(242)+310=0RA=47.1kips

Summation of forces along y-direction is equal to 0.

+Fy=0RA+RB5(24)=047.1+RB5(24)=0RB=72.9kips

Consider span BC, find the reactions at the supports:

Summation of moments about C is equal to 0.

MB=0RC(20)5(20)(202)+310=0RC=34.5kips

Summation of forces along y-direction is equal to 0.

+Fy=0RB+RC5(20)=0RB+34.55(20)=0RB=65.5kips

Therefore, the total RB is 72.9+65.5=138.4kips

Find the shear values of the beam:

FA=47.1kips

FB,JL=47.15(24)=72.9kips

FB,JR=47.15(24)+138.4=65.5kips

FC=34.5kips

Find the point of zero shear force for span AB,

Fxx=047.15x=0x=9.42ftfrompointA

For span BC,

Fxx=034.55x=0x=6.9ftfrompointC

Find the moment values of the beam:

MA=0

MB=47.1(24)5(24)(242)=310kipft

MC=0

Mx=9.42ftfrompointA=47.1(9.42)5(9.42)(9.422)=221.8kipft

Mx=6.9ftfrompointC=34.5(6.9)5(6.9)(6.92)=119.025kipft

Sketch the moment distribution results, shear, and moment diagrams of the beam using moment distribution method as shown in Figure 3.

FUNDAMENTALS OF STRUCTURAL ANALYSIS, Chapter 13, Problem 1P , additional homework tip  4

Therefore, the moment at the support B of the beam using approximate analysis is 360kipft_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Recommended textbooks for you
  • Structural Analysis
    Civil Engineering
    ISBN:9781337630931
    Author:KASSIMALI, Aslam.
    Publisher:Cengage,
    Structural Analysis (10th Edition)
    Civil Engineering
    ISBN:9780134610672
    Author:Russell C. Hibbeler
    Publisher:PEARSON
    Principles of Foundation Engineering (MindTap Cou...
    Civil Engineering
    ISBN:9781337705028
    Author:Braja M. Das, Nagaratnam Sivakugan
    Publisher:Cengage Learning
  • Fundamentals of Structural Analysis
    Civil Engineering
    ISBN:9780073398006
    Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
    Publisher:McGraw-Hill Education
    Sustainable Energy
    Civil Engineering
    ISBN:9781337551663
    Author:DUNLAP, Richard A.
    Publisher:Cengage,
    Traffic and Highway Engineering
    Civil Engineering
    ISBN:9781305156241
    Author:Garber, Nicholas J.
    Publisher:Cengage Learning
  • Structural Analysis
    Civil Engineering
    ISBN:9781337630931
    Author:KASSIMALI, Aslam.
    Publisher:Cengage,
    Structural Analysis (10th Edition)
    Civil Engineering
    ISBN:9780134610672
    Author:Russell C. Hibbeler
    Publisher:PEARSON
    Principles of Foundation Engineering (MindTap Cou...
    Civil Engineering
    ISBN:9781337705028
    Author:Braja M. Das, Nagaratnam Sivakugan
    Publisher:Cengage Learning
    Fundamentals of Structural Analysis
    Civil Engineering
    ISBN:9780073398006
    Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
    Publisher:McGraw-Hill Education
    Sustainable Energy
    Civil Engineering
    ISBN:9781337551663
    Author:DUNLAP, Richard A.
    Publisher:Cengage,
    Traffic and Highway Engineering
    Civil Engineering
    ISBN:9781305156241
    Author:Garber, Nicholas J.
    Publisher:Cengage Learning