menu
bartleby
search
close search
Hit Return to see all results
close solutoin list

The rotor shaft of a helicopter (see figure part a) drives the rotor blades that provide the lifting force and is subjected to a combination of torsion and axial loading (sec figure part b), It is known that normal stress y = 68 MPa and shear stress t = —100 MPa. Using Mohr's circle, determine the following: (a) The stresses acting on an element oriented at a counterclockwise angle 9 = 22,5° from the x axis, (b) Find the maximum tensile stress, maximum compressive stress, and maximum shear stress in the shaft.Show all results on sketches of properly oriented elements.

BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

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

Solutions

Chapter
Section
BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.4.10P
Textbook Problem
368 views

The rotor shaft of a helicopter (see figure part a) drives the rotor blades that provide the lifting force and is subjected to a combination of torsion and axial loading (sec figure part b),

It is known that normal stress y = 68 MPa and shear stress t = —100 MPa. Using Mohr's circle, determine the following:

(a) The stresses acting on an element oriented at a counterclockwise angle 9 = 22,5° from the x axis,

(b) Find the maximum tensile stress, maximum compressive stress, and maximum shear stress in the shaft.Show all results on sketches of properly oriented elements.

  Chapter 7, Problem 7.4.10P, The rotor shaft of a helicopter (see figure part a) drives the rotor blades that provide the lifting

(a)

To determine

The stress acting on the element oriented at a counter-clockwise angle 22.5 .from the x-axis.

Explanation of Solution

Given information:

Normal stress acting along y-axis is 68MPa , shear stress along xy-plane is 100MPa and orientation of element from x-axis in counter-clockwise is 22.5° .

The following are the steps to draw the Mohr s circle

  1. Draw the x-axis and y-axis and indicate the origin as point O (0,0) . Here x-axis denotes normal stress and y-axis denotes shear stress.
  2. Write the expression to locate the center point the circle from the origin (ie., OC). Mark the point A on origin (0,0) Here point A and point O coincide with each other.
  3. OC=σx+σy2....... (I)

    Here, the stress along x-axis is σx and along y-axis is σy

  4. Show the point B on x-axis at (68,0)
  5. Draw a perpendicular line of a length equal to 100 units from point A in upward direction and mark point D as end point.
  6. For the radius of Mohr s circle, extend a line from D to C. ie., radius is equal to DC.
  7. To calculate stresses on an element oriented at angle θ form the x-axis, rotate the x-axis by angle 2θ .

The following figure shows the Mohr s circle:

  

     Figure-(1)

The following observations are considered from figure-(1):

  OD=100unitsCB=34unitsFB=100unitsOC=34units

From figure-(1) OC is equal to normal average stress ie., ( σavg=34MPa ).

Write the expression for principle angle.

  2θp=tan1(FBCB)....... (I)

Here, principle plane angle is θp .

Write the expression for radius of the Mohr s circle.

  R=OC2+OD2 (II)

Here, radius of the Mohr s circle is R , the distance between O and D is OD and the distance between O and C is OC .

Write the expression for the stress acting on element along x -direction.

  σx=σavgRcos(2θp2θ)....... (III)

The stress acting on element in x -direction is σx .

Write the expression for the stress acting on element along y -direction.

  σy=σavg+Rcos(2θp2θ) . (IV)

Here, the stress acting on element along y -direction is σy

The shear stress acting on element along x-y plane.

  τxy=Rsin(2θp2θ)....... (V)

Here, shear stress acting on element along x-y plane is τxy .

Calculation:

Substitute 100units for FB and 34units for CB.in Equation (I).

  2θp=tan1(100units34units)=tan1(2

(b)

To determine

The principle stress

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 7 Solutions

Mechanics of Materials (MindTap Course List)
Show all chapter solutions
add
Ch. 7 - The polyethylene liner of a settling pond is...Ch. 7 - Solve the preceding problem if the norm al and...Ch. 7 - Two steel rods are welded together (see figure):...Ch. 7 - Repeat the previous problem using ? = 50° and...Ch. 7 - A rectangular plate of dimensions 3.0 in. × 5.0...Ch. 7 - Solve the preceding problem for a plate of...Ch. 7 - A simply supported beam is subjected to point load...Ch. 7 - Repeat the previous problem using sx= 12 MPa.Ch. 7 - At a point on the surface of an elliptical...Ch. 7 - Solve the preceding problem for sx= 11 MPa and...Ch. 7 - An clement m plane stress from the frame of a...Ch. 7 - Solve the preceding problem for the element shown...Ch. 7 - : A gusset plate on a truss bridge is in plane...Ch. 7 - The surface of an airplane wing is subjected to...Ch. 7 - At a point on the web of a girder on an overhead...Ch. 7 - -26 A rectangular plate of dimensions 125 mm × 75...Ch. 7 - -27 A square plate with side dimension of 2 in. is...Ch. 7 - The stresses acting on an element are x= 750 psi,...Ch. 7 - Repeat the preceding problem using sx= 5.5 MPa....Ch. 7 - An element in plane stress is subjected to...Ch. 7 - -4. - An element in plane stress is subjected to...Ch. 7 - An element in plane stress is subjected to...Ch. 7 - The stresses acting on element A in the web of a...Ch. 7 - The normal and shear stresses acting on element A...Ch. 7 - An element in plane stress from the fuselage of an...Ch. 7 - -9The stresses acting on element B in the web of a...Ch. 7 - The normal and shear stresses acting on element B...Ch. 7 - ‘7.3-11 The stresses on an element are sx= -300...Ch. 7 - - 7.3-12 A simply supported beam is subjected to...Ch. 7 - A shear wall in a reinforced concrete building is...Ch. 7 - The state of stress on an element along the...Ch. 7 - -15 Repeat the preceding problem using ??. = - 750...Ch. 7 - A propeller shaft subjected to combined torsion...Ch. 7 - 3-17 The stresses at a point along a beam...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - -18 through 7.3-22 An element in plane stress (see...Ch. 7 - At a point on the web of a girder on a gantry...Ch. 7 - The stresses acting on a stress element on the arm...Ch. 7 - The stresses at a point on the down tube of a...Ch. 7 - An element in plane stress on the surface of an...Ch. 7 - A simply supported wood beam is subjected to point...Ch. 7 - A simply supported wood beam is subjected to point...Ch. 7 -   Ch. 7 - .4-2 An element in uniaxial stress is subjected to...Ch. 7 - An element on the gusset plate in Problem 7.2-23...Ch. 7 - An element on the top surface of the fuel tanker...Ch. 7 - An element on the top surface of the fuel tanker...Ch. 7 - An element in biaxial stress is subjected to...Ch. 7 - • - 7.4-7 An element on the surface of a drive...Ch. 7 - - A specimen used in a coupon test has norm al...Ch. 7 - A specimen used in a coupon test is shown in the...Ch. 7 - The rotor shaft of a helicopter (see figure part...Ch. 7 - An element in pure shear is subjected to stresses...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - An clement in plane stress is subjected to...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - Through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - through 7.4-25 An clement in plane stress is...Ch. 7 - -18 through 7.4-25 An clement in plane stress is...Ch. 7 - 1 A rectangular steel plate with thickness t = 5/8...Ch. 7 - Solve the preceding problem if the thickness of...Ch. 7 - The state of stress on an element of material is...Ch. 7 - An element of a material is subjected to plane...Ch. 7 - Assume that the normal strains x and y , for an...Ch. 7 - A cast-iron plate in biaxial stress is subjected...Ch. 7 - Solve the preceding problem for a steel plate with...Ch. 7 - • - 3 A rectangular plate in biaxial stress (see...Ch. 7 - Solve the preceding problem for an aluminum plate...Ch. 7 - A brass cube of 48 mm on each edge is comp ressed...Ch. 7 - 7.5-11 in. cube of concrete (E = 4.5 X 106 psi. v...Ch. 7 - -12 A square plate of a width h and thickness t is...Ch. 7 - Solve the preceding problem for an aluminum plate...Ch. 7 - A circle of a diameter d = 200 mm is etched on a...Ch. 7 - The normal stress on an elastomeric rubber pad in...Ch. 7 - A rubber sheet in biaxial stress is subjected to...Ch. 7 - An element of aluminum is subjected to tri-axial...Ch. 7 - An element of aluminum is subjected to tri- axial...Ch. 7 - -3 An element of aluminum in the form of a...Ch. 7 - Solve the preceding problem if the element is...Ch. 7 - A cube of cast iron with sides of length a = 4.0...Ch. 7 - Solve the preceding problem if the cube is granite...Ch. 7 - An element of aluminum is subjected to iriaxial...Ch. 7 - Solve the preceding problem if the material is...Ch. 7 - A rubber cylinder R of length L and cross-...Ch. 7 - A block R of rubber is confined between plane...Ch. 7 - -11 A rubber cube R of a side L = 3 in. and cross-...Ch. 7 - A copper bar with a square cross section is...Ch. 7 - A solid spherical ball of magnesium alloy (E = 6.5...Ch. 7 - A solid steel sphere (E = 210 GPa, v = 0.3) is...Ch. 7 - A solid bronze sphere (volume modulus of...Ch. 7 - An element of material in plain strain has the...Ch. 7 - An clement of material in plain strain has the...Ch. 7 - An element of material in plain strain is...Ch. 7 - An element of material in plain strain is...Ch. 7 - A thin rectangular plate in biaxial stress is...Ch. 7 - Solve the preceding problem if b = 180 mm and b =...Ch. 7 - A thin square plate in biaxial stress is subjected...Ch. 7 - Solve the preceding problem if b = 225 mm. x = 845...Ch. 7 - An clement of material subjected to plane strain...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - The strains for an element of material in plane...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - An clement of material in plane strain (see...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - A brass plate with a modulus of elastici ty E = 16...Ch. 7 - Solve the preceding problem if the plate is made...Ch. 7 - An element in plane stress is subjected to...Ch. 7 - Solve the preceding problem for the following...Ch. 7 - During a test of an airplane wing, the strain gage...Ch. 7 - A strain rosette (see figure) mounted on the...Ch. 7 - A solid circular bar with a diameter of d = 1.25...Ch. 7 - A cantilever beam with a rectangular cross section...Ch. 7 - Solve the preceding problem if the cross-...Ch. 7 - A 600 strain rosette, or delta rosette, consists...Ch. 7 - On the surface of a structural component in a...Ch. 7 - - 7.2-26 The strains on the surface of an...Ch. 7 - Solve Problem 7.7-9 by using Mohr’s circle for...Ch. 7 - 7.7-28 Solve Problem 7.7-10 by using Mohr’s circle...Ch. 7 - Solve Problem 7.7-11 by using Mohr’s circle for...Ch. 7 - Solve Problem 7.7-12 by using Mohr’s circle for...Ch. 7 - Solve Problem 7.7-13 by using Mohr’s circle for...Ch. 7 - Solve Problem 7.7-14 by using Mohr’s circle for...

Additional Engineering Textbook Solutions

Find more solutions based on key concepts
Show solutions add
Explain why elastic mounts are used to connect the engine to the frame.

Automotive Technology: A Systems Approach (MindTap Course List)

What is an MCU and what is its function?

Precision Machining Technology (MindTap Course List)

What are some basic database functions that a spreadsheet cannot perform?

Database Systems: Design, Implementation, & Management

Give an example of each of the three types of relationships.

Database Systems: Design, Implementation, & Management

Present Example 8.4 in Chapter 8 using the format discussed in Section 4.2. Divide the example problem into Giv...

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

What is a hacktivist?

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

What are stringer beads?

Welding: Principles and Applications (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)

Why is it important to minimize cable clutter in a rack?

Network+ Guide to Networks (MindTap Course List)