| Stress in Beam |
Determines the internal forces within a beam |
stress = moment*distanceFromNeutralAxis/secondMomentOfArea |
σ = M*c/I |
NewtonPerSquareMeter |
| Shear Force in Beam |
Measures the force that causes parts of a material to slide past each other in opposite directions |
shearForce = ∫(dMoment/dx) dx |
V = ∫(dM/dx) dx |
Newton |
| Bending Moment in Beam |
Calculates the reaction induced in a structural element when an external force is applied, causing the element to bend |
bendingMoment = ∫(shearForce dx) |
M = ∫(V dx) |
NewtonMeter |
| Deflection of Beam |
Calculates the displacement of a point on the beam under load |
deflection = load*length^3 / (48*modulusOfElasticity*secondMomentOfArea) |
δ = PL^3 / (48EI) |
Meter |
| Natural Frequency of Bridge |
Determines the frequency at which the bridge will naturally vibrate |
naturalFrequency = (1/2π) * √(stiffness/mass) |
f_n = (1/2π) * √(k/m) |
Hertz |
| Buckling Load |
Determines the critical load at which a column will buckle |
criticalLoad = π^2*modulusOfElasticity*secondMomentOfArea / (effectiveLengthFactor*length)^2 |
P_cr = π^2*EI / (KL)^2 |
Newton |
| Tensile Strength |
Measures the resistance of a material to breaking under tension |
tensileStrength = load/area |
σ_t = P/A |
NewtonPerSquareMeter |
| Load-Bearing Capacity |
Determines the maximum weight the bridge can hold |
loadBearingCapacity = allowableStress * area |
P = f * A |
Newton |