Mechanics of Materials Chapter 2

For multiaxial loading of a unit cube shown, which of the following expressions represents the deformed length of the edge ab(bar above it)?

(1+ε_z)

Referring to the figure, select all the expressions that are valid for the axial strain ε. L is the original length of the rod, Ld is the length of the rod after the load is applied, and E is the modulus of elasticity.

(Ld-L)/L

The shearing strain shown, γ_xy, can be represented by the change in the _________ of two faces of a unit cube from π/2.

Angle

Fatigue is repeated loading _____ static breaking strength, causing rupture.

Below

The dilatation of a material is defined as the _________, in volume per ________ volume.

Change; Unit

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

Crack

Fatigue is the progressive and localized structural damage that occurs when a material is subjected to _____ loading.

Cyclic

The normal strain of a member is defined as the __________ of the member per unit _________.

Deformation and Length

The Normal Strain of a member is defined as the _______________ of the member per unit __________________________.

Deformation; Length

Referring to the figure shown, if the load P is given, is the bar AB statically determinate or indeterminate?

Determinate

In regard to the unit of the normal strain, what are the appropriate units?

Dimensionless

The difference between engineering and true stress is most apparent for _________________ materials because the cross section area changes more.

Ductile OR Necking

The stress-strain diagram for an idealized _____ material response is shown in the figure.

Elastoplastic

The _____ is the stress for which failure does not occur, even for an indefinitely large number of loading cycles.

Endurance Limit

Saint-Venant's principle assumes that the actual loading and the loading used to compute the stresses must be statically _____.

Equivalent

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

True or false: The elongation of a homogeneous rod raised by ΔT is inversely proportional to the length of the rod and proportional to the temperature change ΔT.

False

True or false: In the stress-strain diagram, the stress σB corresponding to rupture is called the ultimate strength.

False.

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

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

Increase

As shown in the figure, if the length of a member AB is increased while keeping the material the same, the deflection at point E _____.

Increases

As shown in the figure, if the length of a member AB is increased while keeping the material the same, the deflection at point E _______.

Increases

Referring to the figure shown, when an axial force is applied to the post, is the reinforced concrete post statically determinate or indeterminate?

Indeterminate

If a material is perfectly incompressible, the bulk modulus, k, approaches _____.

Infinity

An ______________ material has mechanical properties that are independent of loading direction.

Isotropic

The proportionality constant, G, relating Shear Stress and Strain is called the ___________ of ____________, or equivalently the ___________ Modulus.

Modulus; Rigidity; Shear

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

Necking

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

For a typical ductile material shown in the figure, the elongation during strain-hardening and necking process can be _____ the deformation at yield.

Over 200 Times Larger than

Referring to the alphabet letters used in the figure, the Axial Stress is:

P (Load) / A (Area)

Since the strain ε is a dimensionless quantity, E is expressed in the same units as stress σ—in _____________ or one of its multiples for SI units and in psi or ksi for U.S. customary units.

Pascals

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

Residual

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.

Separately

An equivalent name for modulus of rigidity G is _____ modulus.

Shear

The cubic element shown, deformed only in the xy plane, is in a state of simple _____.

Shear

The figure shown depicts how the circular hole of radius r acts as a _____.

Stress Concentration

To obtain the uniform stress distribution for the loading shown, select the correct statements from the following choices.

Stresses cannot be computed in the immediate vicinity of the points of application of the loads. The plates used must allow the member to freely expand laterally. The actual loading and the loading used to compute the stresses must be statically equivalent. The plates cannot be rigidly attached to the member.

As shown in the figure, to calculate the deformation of the rod BC using the equation δ = PLAEPLAE, where E is the modulus of elasticity, which of the following conditions is necessary?

The Load P should be applied at its ends; The Cross-Sectional Area should be uniform; The Modulus of Elasticity E should be constant

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 _____.

The Same

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

The reactions and internal forces cannot be determined from statics alone. 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.

In regard to a structural member containing a discontinuity such as a hole or a sudden change in cross section, select the correct statements from the following.

The stress-concentration factor is dependent only upon the ratios of the geometric parameters involved. The stresses near the points of application of concentrated loads can reach values much larger than the average value of the stress in the member.

True or False: It is typical to have three independent shear moduli for a fiber-reinforced composite material.

True

True or False: When statics is not sufficient to determine either the reactions or the internal forces, the problems are called statically indeterminate.

True

True or false: The residual stresses in a structure is caused by permanent deformation that can result from either the load stretched beyond the yield point of the material or significant temperature change.

True

True or false: it is possible to have zero axial strain and non-zero axial stress for a homogeneous axial member undergoing a temperature change.

True

The relationship E/2G= 1 + ν among the elastic constants E, G, and ν demonstrates that there are only________ independent constants for a homogeneous isotropic material.

Two

For a homogeneous isotropic elastic solid there are elastic constants E, G, and ν featuring the material response. Among these elastic constants _______ are independent.

Two of them (Remember, E is a constant value)

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.

Width

For linear elastic material response, the proportionality constant E in Hooke's law is known as _____.

Young's Modulus and Modulus of Elasticity

If a material is perfectly incompressible, the dilatation of any deformation is _____.

Zero

In the distribution of stresses in elastoplastic material under increasing load shown in the figure, what is the case where the load is largest that can be applied to the bar without causing plastic deformation?

b (Its right at the point of yield to plastic deformation, but it hasn't expanded to that point yet).

The form of generalized Hooke's law shown is most often associated with ________.

orthotropic materials under multiaxial loading continuous fiber-reinforced composite materials under multiaxial loading

four lines with two loads being figured out is still

statically indeterminate

The reactions and internal forces cannot be determined from statics alone. 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.

δ/L

Match the engineering and true strain with its expressions where ε is the engineering strain, εt is the true strain, δ is the total elongation, and L0 and L are the original and actual length of the gage respectively. ε =______ ε_t =_______

δ/L_0 ; ln(δ/L_0)

Referring to the figure, the Normal Strain at Point Q is defined as:

ε = dδ/dx

A slender bar is under axial loading as shown. If symbols σ_x, σ_y, σ_z represent the normal stresses, and symbols ε_x, ε_y, ε_z are the strains. Select all the nonzero stress and strain components.

σ_x, ε_x, ε_y, and ε_z