Mechanics of materials is easier to revise when each card tests one relationship, definition or condition. A useful deck does not just ask for a formula: it makes you recall what each symbol means, when the equation applies and which assumptions matter.

Work through this deck one card at a time. Read the question, reveal the answer, then grade your recall honestly: mark it low if you could not state the relationship or its conditions; mark it high only if you recalled both accurately. The answers use common mechanics conventions, including tension as positive for normal stress. Check the sign convention used in your course when solving a complete problem.

Work through the deck

In MySummaries, a mechanics of materials deck can sit beside the source notes on the same revision board. Here is one 19-card drill, cut to test core definitions and equations rather than long calculations. The first card is face-up; turn each card to check the answer, then choose the grade that matches how readily you recalled it.

Cards — Mechanics of Materials — Core relationships19 due

For a member under a uniform axial force P, what is the average normal stress over cross-sectional area A?

Average normal stress: σ = P/A. Use a consistent sign convention; tension is commonly positive.

All 19 cards
For a member under a uniform axial force P, what is the average normal stress over cross-sectional area A?Average normal stress: σ = P/A. Use a consistent sign convention; tension is commonly positive.
A 2 m bar extends by 1 mm. What is its engineering normal strain?Engineering strain: ε = ΔL/L₀ = 0.001/2 = 0.0005, or 500 με.
State Hooke’s law for uniaxial linear-elastic response.Hooke’s law: σ = Eε, where E is Young’s modulus. It applies within the linear-elastic range.
How is Poisson’s ratio defined for uniaxial loading?Poisson’s ratio: ν = −εtransverse/εaxial. The minus sign accounts for lateral contraction during tensile extension.
For an isotropic, linear-elastic material, how are E, G and ν related?Elastic moduli relation: G = E/[2(1 + ν)], where G is the shear modulus.
A prismatic bar carries constant axial force P. What is its elastic extension if its length is L and area is A?Axial extension: ΔL = PL/(AE), for a uniform prismatic bar with constant P, A and E.
A straight bar is fully restrained against axial expansion. What thermal stress develops for a temperature rise ΔT?Fully restrained thermal stress: σ = −EαΔT, with tension positive. Heating (ΔT > 0) produces compression; α is the coefficient of thermal expansion.
What is the centroidal second moment of area of a rectangle of width b and depth h about an axis parallel to its width?Rectangle: I = bh³/12. The dimension h is cubed because it is measured perpendicular to the axis.
What is the magnitude of the bending stress at distance y from the neutral axis in an elastic beam?Flexure formula: |σ| = |My|/I, where M is the bending moment and I is the second moment of area about the neutral axis.
Define elastic section modulus S and give the maximum bending-stress relationship.Section modulus: S = I/c, where c is the farthest distance from the neutral axis; maximum elastic bending stress is |σmax| = |M|/S.
What is the beam transverse-shear formula at a point in a cross-section?Transverse shear: τ = VQ/(It), where V is shear force, Q is the first moment of area, I is the second moment of area and t is the local section width.
What is the maximum transverse-shear stress for a solid rectangular section carrying shear force V?Solid rectangle: τmax = 3V/(2A), where A is the cross-sectional area.
What is the elastic torsional-shear stress at radius r in a circular shaft carrying torque T?Circular shaft: τ = Tr/J, where J is the polar second moment of area.
What is the polar second moment of area J for a solid circular shaft of diameter d?Solid circle: J = πd⁴/32.
What is the angle of twist of a uniform circular shaft under constant torque T?Angle of twist: θ = TL/(GJ), with θ in radians when consistent units are used.
For plane stress components σx, σy and τxy, what are the two principal stresses?Principal stresses: σ₁,₂ = (σx + σy)/2 ± √[((σx − σy)/2)² + τxy²].
What is the Euler critical load for an ideal elastic column of length L with effective-length factor K?Euler buckling load: Pcr = π²EI/(KL)². This ideal formula assumes a straight, slender, elastic column with appropriate end restraint represented by K.
For a linearly elastic bar under constant axial load P, what is its strain energy?Axial strain energy: U = P²L/(2AE), for a uniform bar with constant P, A and E.
In a simple uniaxial yield check, how is factor of safety against yielding defined?Yield-based factor of safety: n = σy/σworking, where σy is yield strength and σworking is the applied working stress under the stated uniaxial criterion.
Illustrative 19-card drill on core mechanics of materials relationships.

That is a MySummaries deck, filled with mechanics of materials material. Yours is written from your own notes. Start free

Grade the recall, not the familiarity

A formula can look obvious when it is on the screen and still be difficult to reproduce in a problem. After turning a card, check three things: whether you recalled the equation, whether you identified the variables and units, and whether you named the conditions that limit its use. For example, knowing that τ = VQ/(It) is not enough if you confuse Q with the polar second moment J used in torsion.

Use a low grade when you needed a prompt, mixed up symbols or omitted an important condition. A correct equation recalled promptly earns a stronger grade. If you guessed, treat that as uncertain rather than secure. Spaced repetition is useful only when the grade reflects what you could actually retrieve.

The deck is deliberately broad, but it is not a substitute for working through problems. Practise using the relationships with section properties, sign conventions and consistent units. For a bending problem, identify the neutral axis and the location where stress is requested. For torsion, distinguish the polar second moment of area from the ordinary second moment used in bending. For buckling, check whether the ideal Euler assumptions are appropriate before applying the result.

The core behind the cards

A compact core checklist helps you see whether the deck covers the ideas your notes emphasise. Use it to identify missing topics in your course material, not as a claim that every mechanics of materials syllabus has identical coverage. The four items below collect the relationships most directly represented in the drill.

A board’s must-not-miss core can be arranged like this:

Must not miss coreMechanics of Materials — Core relationships
Axial response: σ = P/A; ε = ΔL/L₀; within linear elasticity, σ = Eε.
Elastic extension and restraint: ΔL = PL/(AE); fully restrained thermal stress σ = −EαΔT for a temperature change ΔT.
Beam response: |σ| = |My|/I; transverse shear τ = VQ/(It); for a solid rectangle τmax = 3V/(2A).
Circular-shaft torsion: τ = Tr/J and θ = TL/(GJ); for a solid circle J = πd⁴/32.
Illustrative core checklist for the relationships tested in the deck.

When a card keeps causing errors, do not simply repeat it until the answer feels familiar. Locate the relevant explanation in your own notes, then make the distinction explicit. A common repair is to write down what the symbol represents: I is the second moment of area for bending, while J is the polar second moment of area for circular-shaft torsion. Another is to state the assumption beside the formula, such as linear elasticity for Hooke’s law or ideal slender-column behaviour for Euler buckling.

Turn repeated errors into a repair task

If the same concept is missed repeatedly, turn it into a short, specific follow-up question. The prompt should make you retrieve the distinction that caused the error, rather than merely repeat the original equation. For example, confusing a thermal strain with a thermal stress is repaired by recalling the free expansion first, then explaining what full restraint changes.

A remediation tray can hold a prompt like this:

Remediation tray

You lost this mark twice: a bar is heated by ΔT. What free thermal strain would it undergo, and what stress develops if its axial expansion is fully restrained? State the sign for heating when tension is positive.

Add cardDismiss
Illustrative repair prompt for a repeated confusion between thermal strain and thermal stress.

Answer that prompt by linking the two steps: free thermal strain is εth = αΔT; full axial restraint prevents the total axial strain from changing, producing σ = −EαΔT in the linear-elastic model. Naming both the free strain and the resulting compressive stress shows that you understand the mechanism, not just the memorised expression.

How MySummaries helps

MySummaries lets you build a revision board from your own mechanics of materials notes, then generate a flashcard deck from that board. You can revisit cards with spaced repetition and use a repeated miss to decide what to repair next. Start from your own material at portal.mysummaries.app.