MAE 373 SB2

If Poisson's ratio is negative, an extensional axial load will _____ the cross section dimensions.

Increase

The proportional constant, G, relating shear stress and strain is called the _____ of _____, or equivalently the _____ modulus.

Modulus Rigidity Shear

An inhomogeneous structure shown is made of steel rods in concrete with perfect bonding. Steel and concrete have different coefficients of thermal expansion. A temperature increase of the unconstrained structure creates _____ strains and _____ stresses.

Nonzero, nonzero. If the structure were homogenous there would be zero stress and zero strain. Here, stress develops between the rods and concrete as they to expand different amounts.

Axial stress is defined as:

P / A -OR- Load / Area -OR- Force / Cross-sectional Area

The equation for engineering stress (sigma) is

P / A Load / Area

The equation for true stress (sigma of t) is

P / A not Load / Original Cross-sectional area

A tensile test specimen has the initial length of 5 in. The final length at rupture is 6.2 in. The percent elongation is ____ %. - 80.6 - 19. 35 - 24 - 21

Percent Elongation = 100 * (LB - L not)/ (L not) 100 * (6.2 - 5) / 5 = 24% 24%

A tensile test specimen has the initial diameter of 5 mm. The minimum diameter measured at rupture is 2.8 mm. The percent reduction in area for the specimen is _____ %. - 68.6 - 44.0 - 218.9 - 55.6

Percent Reduction in area = 100 * (A not - A of b)/ (A not) = 100 * ( pi * (5/2) ^ 2 - pi * (2.8 / 2) ^ 2) /

Hooke's law specifies that the stress is _____ to strain.

Proportional

When stresses remain in a structure that was loaded and unloaded, the remaining stresses are called ____ stresses.

Residual

A member is loaded to 1% elongation. Select all the length and deformation combinations that are consistent with this elongation. - L = 3 ft and (delta) = 0.36 in - L = 24 in and (delta) = 0.20 in - L = 1 m and (delta) = 10 mm - L = 3 m and (delta) = 0.0036 m

The elongation of 1% implies that (delta) = 1% of L. So: - L = 3 ft and (delta) = 0.36 in - L = 1 m and (delta) = 10 mm

T/F: It is possible to have non-zero strain and zero stress for a specimen undergoing a temperature change.

True An unconstrained member expands, but no forces generated.

In the stress-strain diagram, the stress (sigma of u) corresponding to the maximum load applied is called the _____ strength. The stress (sigma of b) corresponding to rupture applied is called the _____ strength.

Ultimate Breaking

Ductile materials, after a maximum value of the load has been reached, will experience the _____ phenomenon while brittle materials do not.

necking

*Image Required* For a typical ductile material (shown in the figure), the elongation during strain-hardening and necking process can be _____ deformation at yield. - Over 200 times larger than - Much less than - Less than - At similar magnitude

over 200 times larger than

*Image Required* In the figure, there's a circular hole in the center of a block with radius r. Radius r acts as a - Stress Concentration -Stress amplifier - Stress Reliever - Load Distributor

Stress Concentration

Modulus of rigidity

Stress/strain A constant relating lateral and axial strain.

A(n) _____ material can have more than one value for its modulus of elasticity. - Anisotropic - Laminate - Composite - Isotropic

- Anisotropic - Laminate - Composite

For linear elastic material response, the proportionality constant E in Hooke's law is known as _____. - Bulk Modulus - Poisson's ratio - Modulus of Elasticity - Young's modulus

- Modulus of Elasticity - Young's Modulus

In regard to stress and strain, which of the following statements are correct?

- The stress-strain diagram can help determine whether the material is ductile or brittle. - The modulus of elasticity can be determined from the stress-strain diagram. - The phenomenon of fatigue can be determined for a material from the stress-strain diagram.

A prismatic rod of 2 meters undergoes 1% elongation. The change in length, (delta), would be _____ meters.

0.02

Fatigue is repeated loading ____ static breaking strength, causing rupture. 1) Below 2) Independent of 3) At the same 4) Above

1) Below

Saint-Venant's principle assumes that the actual loading and the loading used to compute the stresses must be statistically ____. 1) Equivalent 2) Distributed 3) Different 4) Determinant

1) Equivalent

For multiaxial loading of a linear elastic material, the principle of superposition states that the effect of a given combined loading on a structure is obtained by ____ determining the effects of the various loads and combining the results. 1) Separately 2) Approximately 3) Randomly 4) Selectively

1) Separately Superposition combines separate effects to yield the whole response.

In regard to the elastic and plastic behavior of a material, which of the following statements is true? 1) The largest value of stress causing the elastic behavior is called the elastic limit 2) The material will behave elastically and linearly if the stress applied exceeds the yield point 3) Materials behave elastically if the strains in a test specimen from a given load disappears when the load is removed. 4) If the load is removed from a specimen and the strain did not return to 0, this indicates that a plastic deformation has occurred.

1, 3, 4 For 2, the material will behave elastically and linearly if the stress is applied below the yield point.

The form of generalized Hooke's Law shown is most often associated with _____ . 1) Homogeneous isotropic materials under multiaxial loading. 2) Orthotropic materials under multiaxial loading 3) Continuous fiber-reinforced composite materials under multiaxial loading 4) Homogeneous isotropic materials under axial loading.

2, 3

What are the conditions needed for the generalized Hooke's Law under the most general loading case? 1) Material is high Poisson's ratio 2) Material has high modulus of elasticity 3) Material is isotropic 4) Material is homogeneous 5) Material is incompressible

3) Material is isotropic 4) Material is homogeneous

A rod AB of length L placed between two fixed supports as shown is heated. If the length of the rod is doubled, the strain developed in the rod due to the temperature increase will be ____. 1) Halved 2) Doubled 3) The same 4) 4 times higher

3) The same The strain developed in the rod due to the temperature increase is not associated with length

Saint-Venant's principle implies that, at a distance equal to or greater than the ____ of the member, the stress distribution is assumed to be the same regardless of the exact details of the load application. 1) Half of the length 2) Length 3) Width 4) Height

3) Width

In regard to stress and strain, which statements are correct? 1) The phenomenon of fatigue can be determined for a material from the stress-strain diagram 2) Isotropic materials are materials with mechanical characteristics dependent of direction. 3) The modulus of elasticity can be determined from the stress-strain diagram 4) The stress-strain diagram can help determine whether the material is ductile or brittle. 5) The reactions and internal forces cannot be determined from statics alone.

3, 4, 5

The ____ is the stress for which failure does not occur, even for an indefinitely large number of loading cycles. 1) Yield Limit 2) Breaking Limit 3) Elastic Limit 4) Endurance Limit

4) Endurance Limit

Bulk Modulus

A term that describes a substance's resistance to compression under pressure, denoted by the variable B and measured by the ratio of stress (delta P) to strain (delta V/V) Or stiffness. A constant characterizing the change in volume of a material under hydrostatic pressure.

Fatigue failure is usually characterized by a(n) ____ that grows to a size that the undamaged material cannot sustain cyclic loading.

Crack, flaw, defect, imperfection, -OR- rupture

The normal strain of a member is defined as the ____ of the member per unit _____ .

Deformation Length

Unit for normal strain

Dimensionless

*Image Required* The normal strain (epsilon) at point Q is defined as:

Epsilon = (derivative of delta)/(derivative of x)

A designer working on the member shown is interested in the maximum stress, which is found by multiplying the average stress by a stress concentration _____.

Factor or K.

T/F: It is typical to have 3 independent shear moduli for a fiber-reinforced composite material.

False Gxy, Gxz, Gyz are distinct for a fiber-reinforced composites.

T/F: The elongation of a homogeneous rod raised by (delta T) is inversely proportional to the length of the rod and proportional to the temperature change (delta T).

False It is proportional

The phenomenon of _____ causes structural or machine components to fail after a very large number of repeated loadings. - deformation - fatigue - cracking - delamination

Fatigue.

Poisson's Ratio

For elastic deformation, the negative ratio of lateral and axial strains that result from an applied axial stress. Also a constant.

Two bars having identical cross-sectional area and modulus of elasticity, but different coefficient of thermal expansion, are constrained between the same rigid supports as shown in the illustration. The bar with the higher coefficient of thermal expansion will have ____ stress and _____ strain when the temperature is raised.

Higher, zero