   # A simply supported beam is subjected to the end couples (bending is about the strong axis) and the axial load shown in Figure P6.6-5. These moments and axial load are from service loads and consist of equal parts dead load and live load. Lateral support is provided only at the ends. Neglect the weight of the beam and investigate this member as a beamâ€”column. Use F y = 50 ksi. a. Use LRFD. b. Use ASD. ### Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
Publisher: Cengage Learning
ISBN: 9781337094740

#### Solutions

Chapter
Section ### Steel Design (Activate Learning wi...

6th Edition
Segui + 1 other
Publisher: Cengage Learning
ISBN: 9781337094740
Chapter 6, Problem 6.6.5P
Textbook Problem
124 views

## A simply supported beam is subjected to the end couples (bending is about the strong axis) and the axial load shown in Figure P6.6-5. These moments and axial load are from service loads and consist of equal parts dead load and live load. Lateral support is provided only at the ends. Neglect the weight of the beam and investigate this member as a beamâ€”column. Use F y = 50 ksi.a. Use LRFD.b. Use ASD. To determine

(a)

If the member is a beam-column using LRFD method.

### Explanation of Solution

Given data:

The factored bending moment is 60ft-k.

Concept used:

Write the equation that satisfies AISC specification by using LRFD method.

Pu2ϕbPn+(MuxϕbMnx+MuyϕbMny)1.0

Here, the compressive design strength is ϕbPn, the factored axial load is Pu the flexural load about xaxis is Mux, the nominal flexural strength about xaxis is ϕbMnx, the flexural load about yaxis is Muy, and the nominal flexural strength about yaxis is ϕbMny.

Calculation:

Write the expression for axial factored load Pu on the member.

Pu=1.6PL+1.2PD (I)

Substitute 16k for PL and 16k for PD in Equation (I).

Pu=(1.6×16k)+(1.2×16k)=25.6k+19.2k=44.8k

Write the expression for factored bending moment.

Mnt=1.6ML+1.2MD (II)

Here, the factored bending moment of dead load is MD, the factored bending moment of live load is ML, and the factored bending moment of the load is Mnt.

Substitute 30ft-k for MD and 30ft-k for ML in Equation (II).

Mnt=1.6(30ft-k)+1.2(30ft-k)=84ft-k

Write the expression for the factor Cm.

Cm=0.60.4(M1M2) (III)

Here, the moment which has lesser value is M1 and the moment which has higher value is M2

Substitute 84ft-k for M1 and 84ft-k for M2 in Equation (III).

Cm=0.60.4(84ft-k84ft-k)=0.60.4(1)=0.6+0.4=1.0

Write the formula for calculating buckling stress.

Pe=π2EI(KL/r)2 (IV)

Here, the steels elastic modulus is E, the sections moment of inertia about the major principal axis is I and the members effective length about is KL/r.

Substitute 29000ksi for E, 171in4 for I, 10ft for KL/r in Equation (IV).

Pe=π2(29000ksi)(171in4)((10ft)(12inch1ft))2=48943368.23k-in214400in2=3399k

Write the expression for moment amplification factor.

B1=Cm1(αPuPe) (V)

Here, the modification factor is Cm, Eulers buckling stress is Pe, and the factored axial load is Pu

To determine

(b)

If the member is a beam-column using ASD method.

### 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

Find more solutions based on key concepts
A car has a mass of 1500 kg. Express the mass and the weight of the car using BG and U.S. Customary units. Show...

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

What are three typical reasons why companies develop their own information systems?

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

Wheel A: 32A60H8V Wheel B: 39C100L6V Which wheel is finer?

Precision Machining Technology (MindTap Course List)

What is incident classification?

Management Of Information Security

What are vulnerabilities? How do you identify them?

Principles of Information Security (MindTap Course List)

What is the kernel of the operating system?

Principles of Information Systems (MindTap Course List)

Describe a server operating system. List examples of server operating systems.

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)

Name three items that are manufactured using welding.

Welding: Principles and Applications (MindTap Course List) 