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 D, Problem 4P
Textbook Problem
180 views

Determine the reactions and draw the shear and bending moment diagrams for the beams shown in Figs. PD.1 through PD.8 using the three-moment equation.

Chapter D, Problem 4P, Determine the reactions and draw the shear and bending moment diagrams for the beams shown in Figs.

To determine

Calculate the reactions for the given beam.

Sketch the shear and bending moment diagrams for the given beam.

Explanation of Solution

Given information:

The structure is given in the Figure.

Apply the sign conventions for calculating reactions 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:

Find the degree of indeterminacy of the structure:

Degree of determinacy of the beam is equal to the number of unknown reactions minus the number of equilibrium equations.

The beam is supported by 4 support reactions and the number of equilibrium equations is 3.

Therefore, the degree of indeterminacy of the beam is i=1.

Select the bending moment MB at the interior support B as redundant.

Consider the supports A', A, and B as l, c, and r respectively.

Express the general three-moment equation as shown below:

MlLlIl+2Mc(LlIl+LrIr)+MrLrIr=[PlLl2klIl(1kl2)PrLr2krIr(1kr2)wlLl34IlwrLr34Ir6E(ΔlΔcLl+ΔrΔcLr)]        (1)

Here, Mc is the bending moment at support c, Ml,Mr are the bending moments at the adjacent supports to the left and to the right of c, E is the modulus of elasticity, Ll,Lr are the lengths of the spans to the left and to the right of c, Il,Ir are the moments of inertia of the spans to the left and to the right of c, Pl,Pr are the concentrated loads acting on the left and the right spans, kl or kr is the ratio of distance of Pl or Pr from the left or right support to the span length, wl,wr are the uniformly distributed loads to the left and right spans, Δc is the settlement of support c, Δl,Δr is the settlement of adjacent supports to the left and to the right of c,

Sketch the equivalent beam for analysis of three-moment equation as shown in Figure 1.

Refer to Figure 1.

The moment at A' is MA'=0.

Find the moment at B,

MB+15(7)(72)=0MB=367.5kNm

Apply three-moment equation at joint A,

Substitute 367.5kNm for MB, 0 for Ll, 7 m for Lr 0 for Il, I for Ir, 0 for Pl, 0 for Pr, 0 for kl, 0 for kr, 0 for wl, 15kN/m for wr, and 0 for Δc,Δl,Δr in Equation (1)

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 Textbook Solutions

Find more solutions based on key concepts
Show solutions add
VocabularyAs a well-educated engineer and intelligent citizen, it is important for you to understand that you n...

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

State the purpose of a hot spot, and list tips for using hot spots safely.

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

What e the main principles of source document design?

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

Identify three reasons for increased spending on data centers.

Principles of Information Systems (MindTap Course List)

Describe the type(s) of relationship(s) between STORE and REGION.

Database Systems: Design, Implementation, & Management

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

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

List some applications that use high-pressure piping.

Welding: Principles and Applications (MindTap Course List)