BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

Solutions

Chapter
Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 15, Problem 17P
Textbook Problem
157 views

Determine the member end moments and reactions for the frames shown in Figs. P15.17–P15.20 by using the slope-deflection method.

Chapter 15, Problem 17P, Determine the member end moments and reactions for the frames shown in Figs. P15.17P15.20 by using

FIG. P15.17, P15.21

To determine

Find the member end moments and reaction for the frames.

Explanation of Solution

Fixed end moment:

Formula to calculate the fixed moment for UDL is WL212.

Formula to calculate the fixed moment for point load with equal length are PL8.

Calculation:

Consider the flexural rigidity EI of the frame is constant.

Show the free body diagram of the entire frame as in Figure 1.

Refer Figure 1,

Calculate the fixed end moment for AC.

FEMAC=75×68=56.25kNm

Calculate the fixed end moment for CA.

FEMCA=56.25kNm

Calculate the fixed end moment for CD.

FEMCD=25×(9)212=168.75kNm

Calculate the fixed end moment for EC.

FEMDC=168.75kNm

Calculate the slope deflection equation for the member AC.

MAC=2EIL(2θA+θC3ψ)+FEMAC

Substitute 0 for ψ, 0 for θA, 6 m for L and 56.25kNm for FEMAC.

MAC=2EI6(2(0)+θC3(0))+56.25=0.333EIθC+56.25        (1)

Calculate the slope deflection equation for the member CA.

MCA=2EIL(2θC+θA3ψ)+FEMCA

Substitute 0 for ψ, 0 for θA, 6 m for L and -56.25kNm for FEMCA.

MCA=2EI6((0)+2θC3(0))56.25=0.667EIθC56.25        (2)

Calculate the slope deflection equation for the member CD.

MCD=3EIL(θC+2θD3ψCD)+FEMCD+FEMCD2

Substitute 0 for ψ, 0 for θD, 9 m for L, and 168.75kNm for FEMCD.

MCD=3EI9(0+θC3(0))+168.75+168.752=0.333EIθC+253.13        (3)

Calculate the slope deflection equation for the member DC.

MDC=0

Write the equilibrium equation as below.

MCA+MCD=0

Substitute equation (2) and equation (3) in above equation

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

Chapter 15 Solutions

Structural Analysis
Show all chapter solutions
add

Additional Engineering Textbook Solutions

Find more solutions based on key concepts
Show solutions add
What are the equivalent annual worth and future worth of the cash flow given in Problem 20.15? Assume i = 8%.

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

Describe client/server architecture, including fat and thin clients, client/server biers, and middleware.

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

Briefly define quality control and explain its purpose.

Precision Machining Technology (MindTap Course List)

What are cryptography and cryptanalysis?

Principles of Information Security (MindTap Course List)

Problematic Camera After charging your digital camera battery overnight, you insert the battery and turn on the...

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

If your motherboard supports ECC DDR3 memory, can you substitute non-ECC DDR3 memory?

A+ Guide to Hardware (Standalone Book) (MindTap Course List)