CIV-00 · laboratory
Euler buckling, beam flexure, Mohr, transformed RC, influence lines and the method of joints.
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32 governing sheets
Critical compressive load of a slender elastic column.
StabilityBending stress σ = My/I in a slender beam.
FlexureIn-plane principals from σx, σy and τxy.
Stress stateModular ratio n = Es/Ec converts steel to equivalent concrete.
Reinforced concreteSimply supported beam: δ = 5 w L⁴ / (384 EI).
DeflectionHorizontal shear τ = VQ /(I t) in a beam web.
ShearShear τ = T r / J and twist θ = T L /(G J).
TorsionI = Icm + A d² about a parallel axis.
Section propertiesExtreme-fibre stress σ = P/A ± M y / I.
Combined stressVertical bar of a symmetric triangular truss: N = F / (2 sin θ).
Trussδ = P L /(A E) and σ = E ε for a prismatic bar.
Elasticityf = Z/W; rectangle gives f = 1.5.
Plasticityσ1,2 = (σx+σy)/2 ± √[((σx−σy)/2)² + τxy²]. The circle's far and near poles.
StressMp = fy Z. For a rectangle Z = bh²/4 so Mp = fy b h²/4.
Plasticityn = Es/Ec. Steel area becomes n As in the concrete modular ratio.
Reinforced concreteMa = P a b / L at a section from the left support. Influence ordinate η = a b / L for P = 1.
InfluenceΔ = N n L / (A E). Real force N, virtual n from a unit dummy load.
EnergyS = I / c, σ = M / S. The extreme-fibre elastic stress.
Flexureτ = V Q / (I t). Jourawski's complementary shear in a beam.
Shearτ = T / (2 Am t). Closed thin-wall tubes, constant shear flow.
Torsionr = √(I/A). The distance at which the area would sit as a thin ring of equal I.
Stabilityλ = K L / r. K encodes fixity: 1 pinned, 0.5 fixed, 2 cantilever.
Stabilitya = As fy / (0.85 f′c b), Mn = As fy (d − a/2). Equivalent rectangular compression.
Reinforced concreteU = P/Pcr + M/Mcr. A linear interaction; U < 1 is the safe side of the diagram.
Stabilityδ = 5 w L⁴ / (384 E I). Simply supported, uniform load.
DeflectionI = b h³ / 12 about the centroidal axis parallel to b.
Geometryfb = M / S. Allowable-stress snapshot; compare fb to 0.66 Fy (AISC ASD vintage).
Steelσ = P/A ± P e c / I. Decompression when the tensile bit cancels P/A.
Prestressq = V Q / I. Force per unit length at a glued or welded joint.
Shearτmax = √[((σx−σy)/2)² + τxy²], θp = ½ atan2(2τxy, σx−σy).
StressPcr = π² EI / (K L)². The first eigenvalue of a slender column.
Stabilityσ = M y / I. Navier's hypothesis: plane sections remain plane.
Flexure