A 600 strain rosette, or delta rosette, consists of three electrical-resistance strain gages arranged as shown in the figure. Gage A measures the normal strain e, in the direction of the x axis. Gages Band C measure the strains and e in the inclined directions shown. Obtain the equations for the strains 8. e. and y, associated with the x-v axes.

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.7.24P
Textbook Problem
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A 600 strain rosette, or delta rosette, consists of three electrical-resistance strain gages arranged as shown in the figure. Gage A measures the normal strain e, in the direction of the x axis. Gages Band C measure the strains and e in the inclined directions shown. Obtain the equations for the strains 8. e. and y, associated with the x-v axes.

To determine

The equation for the strain in the x direction.

The equations for the strain in the y direction.

The equation of the shear strain associated with x y axes.

Explanation of Solution

The following figure shows the 60 ° strain rosette having three electrical resistance.

b

Figure-(1)

From figure (1)

At resistor A the angle θ is zero and Strain is ε A . At resistor B the angle is 60 ° and strain is ε B . At resistor C the angle is 120 ° and the strain is ε C .

For θ = 0 °

ε x = ε A

Write the expression for the normal strain at an angle of 60 ° from the horizontal.

ε B = ε x + ε y 2 + ε x ε y 2 cos 2 θ + γ x y 2 sin 2 θ .....(I)

Here, the strain at an angle of 60 ° from the horizontal is ε B , the strain in the x direction is ε x , the strain in the y direction is ε y , the shear strain is γ x y and the angle between resistor A and B is θ .

Substitute 60 ° for θ and ε A for ε x in Equation (I).

ε B = ε A + ε y 2 + ε A ε y 2 cos ( 2 × 60 ° ) + γ x y 2 sin ( 2 × 60 ° ) ε B = ε A + ε y 2 ( ε A ε y 4 ) + γ x y 3 4 ε B = ε A 4 + 3 ε y 4 + γ x y 3 4 .....(II)

Write the expression for the normal strain at an angle of 120 ° from the horizontal.

ε C = ε x + ε y 2 + ε x ε y 2 cos 2 θ + γ x y 2 sin 2 θ .....(III)

Here, the strain in the resistor C is ε C .

Substitute 120 ° for θ and ε A for ε x in Equation (III)

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