Theory Quiz

Understanding the Physics of Structural Mechanics ITC

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1 / 45

In a uniaxial stress-strain test, necking is generally observed before failure for which type of material? Select the best option.

Ductile metals

Concrete

Ceramics

Glass

2 / 45

Which of the following components are shear stress components? Choose three best options.

$\sigma_{yz}$

$\sigma_{yy}$

$\sigma_{xy}$

$\sigma_{yx}$

3 / 45

Consider the natural frequency of a single degree-of-freedom spring-mass system. What will be the ratio of the natural frequency of this system on earth compared to that of the system on the moon? Note that gravity on earth is ~ 6 times than that on the moon.

$\sqrt(1/6)$

1

$\sqrt(6)$

Infinite

4 / 45

Which of these properties dissipates energy from a system? Select the best option.

Mass

Damping

Elastic strain

Stress

5 / 45

What is the most appropriate analysis type to use when simulating two cars crashing in to each other?

Time- history dynamics analysis

Harmonic analysis

Static analysis

Modal analysis

6 / 45

Which assumption best explains why a rotating shaft might appear to expand radially when small deformation formulation is used ?

$F_{_{c}}=\frac{mv^{2}}{r}$

$cos^{2}(\theta )+sin^{2}(\theta )=1$

$cos(\theta )\approx 1,sin(\theta )\approx \theta $

$\varepsilon = \int \frac{dl}{l}$

7 / 45

Which of the following derived quantities is always a positive value?

Equivalent Strain

Normal Strain

Shear Strain

Principal Strain

8 / 45

Consider two masses connected by a single spring, and the masses are only allowed movement in a single direction (1D). How many natural frequencies are there in this system?

4

1

2

3

9 / 45

Why are frequency domain analyses preferred over time domain analyses?

Frequency domain analyses are easier to set up when nonlinear contact between bodies is important.

Frequency domain analyses are more accurate compared to time domain analyses when loads are nonsinusoidal

Frequency domain analyses are easier to solve when nonlinear materials have a significant influence on the response.

Frequency domain analyses are much more computationally efficient compared to time domain analyses

10 / 45

There are two cases of principal stresses: case 1 has $s_1$ = 20 MPa, $s_2$ = 0, $s_3$ = 0 while case 2 has $s_1$ = 40 MPa, $s_2$ = 40 MPa, $s_3$ = 20 MPa. Which of the following statements are correct? Choose two best options.

The equivalent stress calculated from case 2 is the larger than the one calculated from case 1.

The equivalent stress calculated from case 1 is the same as the one calculated from case 2.

These three stress states are on the different cylindrical surfaces in principal stress space.

These two stress states are on the same cylindrical surface in principal stress space.

11 / 45

Which of the following equations defines 1D engineering strain?

$\epsilon=\int \frac{\mathrm{d} l}{l}$

$\sigma =E\epsilon $

$\epsilon=\Delta l/l_{o}$

$\epsilon _{ij}=\frac{1}{2}\left ( u_{i,j} + u_{j,i}\right )$

12 / 45

Why does large deformation introduce nonlinearity in the model?

Large deformation makes material behavior nonlinear

Large deformation results in rigid body motion

Large deformation alone does not introduce nonlinearity in the model

Large deformation results in change in shape which can change the direction of loading

13 / 45

For structures that undergo vibrations under a constant load, the pre-stress state is often included in a modal analysis because _____. Select the best option to complete the sentence.

doing so will help in avoiding zero-natural frequencies

doing so will impact the applied boundary conditions

the stress state changes the natural frequency of a structure

doing so will change the structure's length

14 / 45

If we consider the inertial effects in a system, which of the terms from governing equations would it impact? The equations of motion are given by this equation:

$\left [ M \right ]\left \{ \ddot{u} \right \} + \left [ C \right ]\left \{ \dot{u} \right \} + \left [ K \right ]\left \{ u \right \} = F\left \{ t \right \}$

$\left [ K\right ]\left \{ {u} \right \}$

$F\left \{ t \right \}$

$\left [ M \right ]\left \{ \ddot{u} \right \}$

$\left [ C\right ]\left \{ \dot{u} \right \}$

15 / 45

Which unit represents a measure of strain?

$mm/mm$

$\mu\epsilon$

$N/mm$

$N.mm/mm^{2}$

16 / 45

Which results can be obtained from mechanical simulations of flexible bodies under applied loads? Choose three correct options.

Stresses and strains

Deformations

Intermolecular forces

Reaction forces

17 / 45

What is the primary reason for fluid sloshing in a tanker truck during transportation?

Vibrations due to road roughness

Inertia of motion of the fluid

Vibrations due to IC engine operation

Fluids do not slosh inside a tanker

18 / 45

The selected material for an engineered design is a metal. The material response behaves in a linear manner up until the yield point, after which the response is nonlinear with permanent deformation. Select the two most reasonable assumptions that can be made in a finite element analysis to calculate an accurrate strain field during operation.

During operation, if it is not known how much strain will be experienced by the material, it is reasonable to use nonlinear material behavior in the analysis.

During operation, if it is not expected that the material yields or undergoes permanent deformation, it is reasonable to use linear material behavior in the analysis.

During operation, if the expected deformation is relatively small, it is reasonable to use linear material behavior in the analysis.

Unless the designed part fails in operation, it is reasonable to use linear material behavior in the analysis.

19 / 45

When we place a dead weight on top of a viscoelastic material sample, what phenomenon do we expect to see?

Stress stiffening

Strain hardening

Stress relaxation

Creep

20 / 45

Consider a situation where there are two geometrically identical brackets, each made with a different grade of plastic that have different elastic moduli (stiffness). Both brackets are constrained and loaded in the same manner. Select two statements which are true, assuming linear response.

The location of maximum deformation of either bracket will depend on their elastic modulus (stiffness) value.

The magnitude of maximum strain will be the same for both brackets.

The location of maximum deformation will be the same on both brackets.

The location of maximum strain will be the same on both brackets.

21 / 45

Lagrange strain formulation is best characterized as _____. Select the best option to complete the statement.

another form of Hooke's Law

an example of small strain theory

another form of isotropic hardening

an example of finite strain theory

22 / 45

Which type of analysis should be performed if we're interested in studying the response of a building to a specific earthquake profile?

Steady-state analysis

Time-domain analysis

Frequency-domain analysis

Topological Optimization

23 / 45

Select the phrase that best describes the nonlinear nature of contact.

A changing status nonlinearity

Always a closed and sliding status

Always a closed and sticking status

Always an open status

24 / 45

For a typical static analysis, what are some common ways of evaluating possible material failure? Choose two best options.

Examine strain results.

Examine displacement results.

Examine reaction force results.

Examine stress results.

25 / 45

A continuous system will have how many natural frequencies?

>10 and <100

Infinite

6

>6 and <10

26 / 45

When a load is graphically represented in a transient analysis, the load is plotted against ____. Select the best option to complete the sentence.

amplitude

wavelength

frequency

time

27 / 45

When we clamp and hold a viscoelastic material sample under a constant amount of displacement, what phenomenon do we expect to see?

Creep

Stress stiffening

Strain hardening

Stress relaxation

28 / 45

Mode Participation factor and effective mass measure _____. Select the best option to complete the sentence.

the stiffness change in each direction

the amount of mass moving in each direction for each mode

It just measures the highest value

It just specifies the direction of excitation of mass and nothing more

29 / 45

A dog bone tensile test of polyethylene illustrates which two types of nonlinearites?

Nonlinear Contact

Spin Softening

Nonlinear Material

Large Deformation

30 / 45

Consider the case where we want to determine the maximum lateral deformation of a suspension bridge when subjected to oscillating wind loads at a given frequency. Which analysis type would be most appropriate for this situation?

Rigid body analysis

Time- history dynamics analysis

Static analysis

Harmonic analysis

31 / 45

Select the three best options that are needed to prepare an engineering problem for simulation.

Isolate a single part from an assembly to analyze

Decide what kind of material model should be used and obtain proper material parameters

Select appropriate loads and boundary conditions to represent the real-life situation

Determine the necessary geometric details to include in the model

32 / 45

If we introduce time-dependent material stiffness in a system, which of the terms from governing equations would it impact? The equations of motion are given by this equation:

$\left [ M \right ]\left \{ \ddot{u} \right \} + \left [ C \right ]\left \{ \dot{u} \right \} + \left [ K \right ]\left \{ u \right \} = F\left \{ t \right \}$

$\left [ C\right ]\left \{ \dot{u} \right \}$

$\left [ K\right ]\left \{ {u} \right \}$

$F\left \{ t \right \}$

$\left [ M \right ]\left \{ \ddot{u} \right \}$

33 / 45

What is the best way to determine if an analysis needs to include large deformation effects?

Calculate with small deformation and large deformation formulas and compare.

Always use large deformation formula to be conservative

Only use large deformation formulation when strain components exceed 5%

Only use large deformation when convergence becomes an issue

34 / 45

Consider a one-dimensional bar with one end fixed while the other end has been extended by a displacement of $u_{0}$. The length of the bar = $L$. The one-dimensional stiffness of the material is $E$. If the strain over the bar is $u_{0}/L$, what is the stress over the bar? Choose the best option.

$\frac{Eu_{0}}{L/2}$

$Eu_{0}$

$Eu_{0}/L$

$Eu_{0}L$

35 / 45

Volumetric expansion occurs when all shear strain components are zero and all normal strain components are equal to each other (i.e., $e_{xy}=e_{xz}=e_{yz}=0$ but $e_{xx}=e_{yy}=e_{zz}$). Select the correct statement.

Equivalent strain will be equal to the normal strain.

Equivalent strain is zero when there is only volumetric expansion.

Equivalent strain cannot be determinned without additional information regarding the deformation.

Equivalent strain will be equal to twice the normal strain.

36 / 45

What type of analysis is preferred for studying the stresses developed in an electronic componenet due to a drop from certain height?

Harmonic analysis

Frequency-domain analysis

Time-domain analysis

Modal analysis

37 / 45

Which of the following statements are correct for stress in solid mechanics? Choose two best options.

Stress is linearly proportional to mechanical strain.

Stress is a measure of force transmission to the interior of continuous bodies.

Stress results can be used to determine if a material reaches its strength limit.

Stress over a body can be calculated by dividing the applied external force by the area under the force.

38 / 45

Which material option best characterizes aluminum prior to yielding?

Nonlinear Elasticity

Hyperelasticity

Linear Elasticity

Metal Plasticity

39 / 45

For any 3 by 3 stress tensor, how can one determine the three principal stresses? Choose two best options.

The three principal stress components are the diagonal components of the stress tensor, which are $\sigma_{xx}$, $\sigma_{yy}$ and $\sigma_{zz}$.

The three principal stress are the normal stresses when the coordinate basis is transformed such that the shear stress components become zero.

The three principal stress components are the three eigenvalues of the stress tensor.

The three principal stress components can be found when the coordinate basis rotates 45 degree from the original position.

40 / 45

Which statement is true about a stress tensor? Choose two best options.

Stress tensor under different coordinate systems represents different stress states.

Stress tensor is not absolute. Under different coordinate systems, its values will be different. However, they all represent the same stress state.

Under different coordinate systems, the components of a stress tensor remain the same values.

A stress tessor is symmetric along the diagonal.

41 / 45

How can one ensure that the number of extracted modes sufficiently characterizes the dynamic response of a system in a modal analysis? Select the best option.

Ratio of effective mass to total mass should be a very large number

Ratio of effective mass to total mass should be ~ 0

Ratio of effective mass to total mass should be ~ 1

Ratio of effective mass to total mass should be ~ 0.5

42 / 45

Which of the following is a characterization of small strain theory?

$\varepsilon = \int \frac{dl}{l}$

$P=-\frac{1}{3}\sigma {_{ii}}$

$\sigma = E\varepsilon$

$\frac{\Delta L}{L}$

43 / 45

Which of the following statements are correct about principal stresses? Choose three best options.

Principal stresses are the components of a stress tensor when its coordinate system is changed in such a way that all shear stress components become zero.

Principal stresses are all normal stresses.

Principal stresses can be used to determine brittle material failure.

The principal stress tensor can have nonzero off-diagonal components.

44 / 45

The process of rolling ductile metals into desired shapes with rigid rollers best exemplifies which of the three types of nonlinearities? Select the best option.

No-separation contact

Material nonlinearities

Nonlinear elastic materials

Internal frictional heating

45 / 45

From the uniaxial tensile test, which of the following is a strain that may represent failure for a component?

Strain at Fracture

Strain at Ultimate Strength

It depends on the type of material tested and its engineering application

Strain at Yield

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Private: Physics of Structural Mechanics

Total time - 60 mins.

Total number of Questions - 45