What does σij represent in a 3×3 stress matrix?

Stress is applied on j face of the material in the +ve i direction

Stress is applied on i face of the material in the +ve j direction

Stress is applied on i face of the material in the -ve j direction

Stress is applied on j face of the material in the +ve i direction

Stress is applied on j face of the material in the -ve i direction

For the following stress matrix, the first invariant of the stress tensor is the trace of a matrix, the sum of diagonal element: I1 = σ11 + σ22 + σ33. The second invariant of matrix is equal to _________\(\begin{vmatrix}\sigma_{11} & \sigma_{12} & \sigma_{13}\\ \sigma_{21}& \sigma_{22} & \sigma_{23}\\ \sigma_{31}& \sigma_{32} & \sigma_{33}\end{vmatrix}\)

Sum of all the elements of the matrix

Sum of all the principal minors of the matrix

Explore topic-wise MCQs in Mechanical Metallurgy.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Mechanical Metallurgy knowledge and support exam preparation. Choose a topic below to get started.

1.	What does σij represent in a 3×3 stress matrix?
A.	Stress is applied on i face of the material in the +ve j direction
B.	Stress is applied on i face of the material in the -ve j direction
C.	Stress is applied on j face of the material in the +ve i direction
D.	Stress is applied on j face of the material in the -ve i direction
Answer» C. Stress is applied on j face of the material in the +ve i direction

Discussion

2.	Calculate the dilation of body, given that the initial volume is 250 mm2 and final volume is 235.5 mm2.
A.	0.058
B.	0.061
C.	0.050
D.	0.060
Answer» B. 0.061

Discussion

3.	Calculate the hydrostatic strain, if εx, εy, εz are 0.01, 0.2, 0.05 respectively?
A.	0.2
B.	0.866
C.	0.125
D.	1
Answer» C. 0.125

Discussion

4.	Experimentally, strain in the material with high precision is measured by _________ method.
A.	calorimetry
B.	hardness testing
C.	bonded wire resistance gauge
D.	microscopy
Answer» D. microscopy

Discussion

5.	The part of strain tensor which involves in the shape change rather than the volume change is called strain deviator ε’ij.
A.	True
B.	False
Answer» B. False

Discussion

6.	For the following stress matrix, the first invariant of the stress tensor is the trace of a matrix, the sum of diagonal element: I1 = σ11 + σ22 + σ33. The second invariant of matrix is equal to _________\(\begin{vmatrix}\sigma_{11} & \sigma_{12} & \sigma_{13}\\ \sigma_{21}& \sigma_{22} & \sigma_{23}\\ \sigma_{31}& \sigma_{32} & \sigma_{33}\end{vmatrix}\)
A.	Sum of all the elements of the matrix
B.	Sum of first column elements
C.	Sum of first raw elements
D.	Sum of all the principal minors of the matrix
Answer» E.

Discussion

7.	The number of components required to define an elastic constant is ______
A.	3
B.	9
C.	27
D.	81
Answer» E.

Discussion

8.	Matrix (2-dimensional arrays) is a second rank tensor.
A.	True
B.	False
Answer» B. False

Discussion

Explore topic-wise MCQs in Mechanical Metallurgy.

What does σij represent in a 3×3 stress matrix?

Calculate the dilation of body, given that the initial volume is 250 mm2 and final volume is 235.5 mm2.

Calculate the hydrostatic strain, if εx, εy, εz are 0.01, 0.2, 0.05 respectively?

Experimentally, strain in the material with high precision is measured by _________ method.

The part of strain tensor which involves in the shape change rather than the volume change is called strain deviator ε’ij.

The number of components required to define an elastic constant is ______

Matrix (2-dimensional arrays) is a second rank tensor.