MAC124: Introduction to Stress, Strain, and Internal Equilibrium

Vocabulary flashcards covering core concepts of engineering statics, internal forces and moments, axial stress and strain, allowable stress design, and factors of safety from the MAC124 course.

Engineering Mechanics

The science that considers the effect of forces upon objects.

Statics

The branch of mechanics that considers objects in equilibrium, in which forces are balanced.

Dynamics

The branch of mechanics that considers objects in motion, in which forces are not balanced.

Two-Dimensional Static Equilibrium

The condition where a body has a resultant force and resultant moment of zero, satisfied by $R_x = \sum F_x = 0$, $R_y = \sum F_y = 0$, and $M_O = \sum M_O = 0$.

Free-Body Diagram (in Solid Mechanics)

A diagram created by cutting a body or part of a body and replacing internal interactions at the cut surface with stress resultants (internal forces and moments) to maintain equilibrium.

Normal Force ($N$)

An internal force that acts perpendicular to the cross-sectional area, developed whenever external loads tend to push or pull on the two segments of a body.

Shear Force ($F$)

An internal force lying in the cross-sectional plane, developed when external loads tend to cause two segments of a body to slide over one another.

Bending Moment ($M$)

An internal moment caused by external loads that tend to bend a body about an axis lying within the plane of the cross section.

Torsional Moment (Torque, $T$)

An internal moment caused by external loads that tend to twist one segment of a body relative to another about an axis perpendicular to the cross section.

Tension (Tensile Load)

A normal force pulling perpendicular to the cross section that causes elongation, conventionally designated with a positive sign ($\sigma > 0$).

Compression (Compressive Load)

A normal force pushing perpendicular to the cross section that causes shortening, conventionally designated with a negative sign ($\sigma < 0$).

Axial Loading

A load applied along the longitudinal axis of a member, which can be either tensile (pulling) or compressive (pushing).

Uniaxial Loading

A special case of axial loading where a structure or material is loaded in only one direction (along a single axis), producing normal stress ($\sigma$) along that axis.

Biaxial Loading

A loading state where loads or stresses are applied along two perpendicular directions simultaneously, such that both stress components $\sigma_x$ and $\sigma_y$ are non-zero.

Centric Axial Load

An axial load whose line of action passes exactly through the centroid of the cross section, producing pure axial stress.

Eccentric Axial Load

An axial load whose line of action does not pass through the centroid of the cross section but is offset by a distance (eccentricity), producing combined axial and bending stresses.

Normal (Axial) Stress ($\sigma$)

The intensity of internal normal force distributed over a cross-sectional area, given by $\sigma = \frac{N}{A}$ with units of Pascals ($\text{Pa} = \text{N/m}^2$).

Normal Strain ($\varepsilon$)

The elongation per unit unloaded (initial) length, calculated as $\varepsilon = \frac{\delta}{L}$, which is a dimensionless quantity often given in microstrain ($\mu\varepsilon$) or percentage ($\%$).

Failure Stress ($\sigma_{\text{fail}}$, Failure Strength)

The maximum stress a material can withstand before breaking or failing, which is an inherent material property independent of cross-sectional area or length under centric axial load.

Allowable Stress ($\sigma_{\text{allow}}$, Allowable Stress Design)

A lower stress limit set below the failure stress used in practical design to prevent failure under service conditions and account for uncertainties.

Factor of Safety ($\text{F.S.}$)

The ratio that determines how much stronger a component is compared to the allowable design limit, defined as $\text{F.S.} = \frac{F_{\text{fail}}}{F_{\text{allow}}} = \frac{\sigma_{\text{fail}}}{\sigma_{\text{allow}}}$.

Stress–Strain Curve

A graphical representation of intrinsic material behavior that normalizes force by area and elongation by length, thereby removing specimen geometry effects present in load–elongation curves.