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Strength of materials · vessels · joints & the shop floor

Mechanics of Materials

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Stress and Strain

  • L1
    Reading the lab report
    which number is a stress, a strain, a modulus, a load
    ★★★★★
    Start
  • L2
    Stress under load
    σ = P/A, asked every way
    ★★★★★
    Start
  • L3
    Strain and stiffness
    ε = δ/L, then the E that prices it
    ★★★★★
    Start
  • L4
    The stretch of a bar
    δ = PL/AE · four sockets, one unknown
    ★★★★★
    Start
  • L5
    Shear and Poisson
    τ = V/A · counting planes · the sideways toll
    ★★★★★
    Start
  • L6
    The elastic family
    E = 2G(1 + ν) · know two, find the third
    ★★★★★
    Start
  • L7
    Margin and heat
    factor of safety · and the stress nobody applied
    ★★★★★
    Start
  • ★
    The Tension Test
    the boss · no calculator · one specimen, read end to end
    ★★★★★
    Start

Torsion and Shafts

  • L9
    The polar moment
    J = πd⁴/32 · why a fourth power punishes a guessed diameter
    ★★★★★
    Start
  • L10
    Shear in the shaft
    τ = Tr/J · the radius, not the diameter
    ★★★★★
    Start
  • L11
    The angle of twist
    φ = TL/JG · radians out, degrees demanded
    ★★★★★
    Start
  • L12
    Torque from power
    T = P/ω · rpm to rad/s first, always
    ★★★★★
    Start
  • L13
    Sizing the shaft
    d = ∛(16T/πτ) · the design direction, then the rack
    ★★★★★
    Start
  • L14
    Keys under shear
    τ = 2T/(dwL) · the cheapest thing in the drive, on purpose
    ★★★★★
    Start
  • ★
    The Drive Line
    the boss · no calculator · motor to key, every link checked
    ★★★★★
    Start

Bending and Beams

  • L16
    The second moment of area
    bh³/12 and πd⁴/64 · why a joist goes on edge
    ★★★★★
    Start
  • L17
    Built-up sections
    the parallel axis theorem, and why the I-beam exists
    ★★★★★
    Start
  • L18
    The section modulus
    S = I/c · one number that rates a beam
    ★★★★★
    Start
  • L19
    The bending moment
    PL/4 against wL²/8 · knowing which beam you have
    ★★★★★
    Start
  • L20
    Stress in bending
    σ = Mc/I, and the shortcut σ = M/S
    ★★★★★
    Start
  • L21
    Shear in the web
    τ = VQ/Ib · and Q, the subtlest given in the course
    ★★★★★
    Start
  • L22
    Deflection limits
    L³, L⁴ and 5/384 · the check that often governs
    ★★★★★
    Start
  • L23
    The cantilever
    PL³/3EI and wL⁴/8EI · held at one end only
    ★★★★★
    Start
  • ★
    The Beam Check
    the boss · no calculator · one joist, moment to margin
    ★★★★★
    Start

Columns, Vessels, Combined Stress

  • L25
    Slenderness
    r = √(I/A) and KL/r · the sorting number of column design
    ★★★★★
    Start
  • L26
    Euler buckling
    Pcr = π²EI/(KL)² · double the length, quarter the capacity
    ★★★★★
    Start
  • L27
    Hoop stress
    σ = pd/2t · the radius-versus-diameter trap
    ★★★★★
    Start
  • L28
    The vessel, two ways
    hoop and longitudinal · and why the hoop is double
    ★★★★★
    Start
  • L29
    Combined stresses
    P/A ± Mc/I · same fibre, one sum, signs decide
    ★★★★★
    Start
  • L30
    Principal stresses
    Mohr's circle as centre plus radius · and the radius is the shear
    ★★★★★
    Start
  • L31
    Stress raisers
    σmax = Kt·σnom · what a hole really costs
    ★★★★★
    Start
  • ★
    The Vessel Audit
    the boss · no calculator · one tank, certified or condemned
    ★★★★★
    Start

Bolts, Welds and the Shop Floor

  • L33
    The thread that holds
    A_t — why a bolt is thinner than the size on its head
    ★★★★★
    Start
  • L34
    Torque and preload
    T = K·D·F — what the wrench actually buys
    ★★★★★
    Start
  • L35
    The preloaded joint
    C and P₀ — the bolt barely notices the load it is holding
    ★★★★★
    Start
  • L36
    The weld throat
    a = 0.707·z, and the capacity that throat buys
    ★★★★★
    Start
  • L37
    Sizing the weld
    the design direction — and the size that goes on the print
    ★★★★★
    Start
  • L38
    Heat input
    what the arc puts in, and what the steel brought with it
    ★★★★★
    Start
  • L39
    Speeds and feeds
    cutting speed is NOT spindle speed
    ★★★★★
    Start
  • L40
    Metal off the bar
    removal rate, pass time, and what speed costs the tool
    ★★★★★
    Start
  • ★
    The Fabrication Order
    the boss · no calculator · one bracket, print to torque wrench
    ★★★★★
    Start

Materials, Fatigue, Fracture

  • L42
    Hardness and grain
    the indent and the microstructure behind it
    ★★★★★
    Start
  • L43
    True stress
    the bar got thinner, and the honest stress got bigger
    ★★★★★
    Start
  • L44
    The Goodman line
    a swing, a mean, and one budget between them
    ★★★★★
    Start
  • L45
    Counting the cycles
    Basquin's line, and Miner's running total
    ★★★★★
    Start
  • L46
    The crack that grows
    K at the tip, and the Paris law it drives
    ★★★★★
    Start
  • L47
    Plastic capacity
    Z, M_p, and the reserve past first yield
    ★★★★★
    Start
  • L48
    Factored loads
    1.2D + 1.6L, and a stiffness from a strength
    ★★★★★
    Start
  • ★
    The Design Review
    the boss · no calculator · one member, signed off or sent back
    ★★★★★
    Start

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