Chapter 11, Problem 11.3.20P

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347

### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
ISBN: 9781337093347
Textbook Problem

# The hoisting arrangement for lifting a large pipe is shown in the figure. The spreader is a steel tubular section with outer diameter 70 mm and inner diameter 57 mm. Its length is 2.6 m, and its modulus of elasticity is 200 GPa.Based upon a factor of safety of 2.25 with respect to Euler buckling of the spreader, what is the maximum weight of pipe that can be lifted? (Assume pinned conditions at the ends of the spreader.)

To determine

The maximum weight of the pipe that can be lifted.

Explanation

Given information:

The outer diameter of the pipe is 70â€‰mm , the inner diameter of the pipe is 57â€‰mm , the length of the pipe is 2.6â€‰m , the modulus of the elasticity is 200â€‰GPa, and the factor of safety is 2.25 .

The figure below shows the free body diagram of hoisting arrangement.

â€ƒâ€ƒ

â€ƒâ€ƒFigure-(1)

Write the expression for the angle subtended by the spreader.

â€ƒâ€ƒtanÎ±=MNON ...... (I)

Here, the distance between point M to N is MN and the distance between point O to N is ON .

Write the expression for force acting along horizontal direction.

â€ƒâ€ƒâˆ‘F hor=0âˆ’pallow+Tcos(Î±)=0T=p allowcos(Î±) ...... (II)

Here, the horizontal force acting on spreader is Tcos(Î±) and the allowable load acting on the spreader is pallow .

Write the expression for force acting along vertical direction.

â€ƒâ€ƒâˆ‘F ver=0Tsin(Î±)âˆ’W max2=0 ...... (III)

Here, the vertical force acting on the spreader is Tsin(Î±) and maximum the weight of the pipe is Wmax .

Substitute pallowcos(Î±) for T in Equation (III).

â€ƒâ€ƒp allowcos(Î±)sin(Î±)âˆ’W max2=0p allowcos(Î±)sin(Î±)=W max2Wmax=2pallowtan(Î±) ...... (IV)

Write the expression for moment of inertia of circular pipe.

â€ƒâ€ƒI=Ï€64[( d 0)4âˆ’( d i)4] ...... (V)

Here, the outer diameter of the pipe is d0 , the inside diameter of the pipe is di .

â€ƒâ€ƒpcr=Ï€2EIL2 ...... (VI)

Here, the youngâ€™s modulus of the pipe is E and the length of the pipe is L .

Write the expression for allowable load.

â€ƒâ€ƒpallow=pcrn ...... (VII)

Here, the factor of safety is n .

Calculation:

Substitute 7 for MN and 10 for ON in Equation (I).

â€ƒâ€ƒtan(Î±)=710tan(Î±)=0.7Î±=tanâˆ’1(0.7)Î±=35Â°

Substitute 70â€‰mm for d0 and 57â€‰mm for di in Equation (V)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

Solve them all with bartleby. Boost your grades with guidance from subject experts covering thousands of textbooks. All for just \$9.99/month

Get As ASAP

#### What is an SPST switch?

Automotive Technology: A Systems Approach (MindTap Course List)

Principles of Information Security (MindTap Course List)

#### List and describe the different types of databases.

Database Systems: Design, Implementation, & Management

#### What is a DBMS, and what are its functions?

Database Systems: Design, Implementation, & Management

#### Explain the differences between a Gantt chart and a PERT/CPM chart

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