# 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.

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

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

### 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.

(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

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