Struts + Intro Flashcards
Statistically determinate beam
The internal forces and moments at any point can be determined solely from the external loads + beam’s geometry. Must be in static equilibrium (net force and net moment acting on it is 0).
Deflection of beams under a load
M / I = σ / y = E / R
M- bending moment
I- second moment of cross sectional area
σ- bending stress
y- distance from neutral axis to position at which stress is calculated.
E- Young’s modulus, measure of how stiff a material is. σ/ε, stress over strain.
R- local radius of curvature of beam
What is a strut
Structural component designed to resist compression/ tension forces. It is typically a slender/ straight member supported at both ends and subjected to axial loads (tend to shorten it). It provides support to a framework.
Buckling , crushing and slenderness.
When a strut is slender, it is more susceptible to BUCKLING: lateral deflection, loss of stability, occurs in long, slender members.
CRUSHING occurs when the material is compressed beyond its yield point (material begins to deform permanently, compression and deformation). Occurs in short, thick members.
SLENDERNESS- important in determining its susceptibility to buckling.
Buckling , crushing and slenderness.
When a strut is slender, it is more susceptible to BUCKLING: lateral deflection, loss of stability, occurs in long, slender members.
CRUSHING occurs when the material is compressed beyond its yield point (material begins to deform permanently, compression and deformation). Occurs in short, thick members.
SLENDERNESS- important in determining its susceptibility to buckling.
What is Euler’s formula used for?
Calculates the critical load (max compressive load a strut can withstand before it becomes unstable and buckles) for a long, slender strut.
Euler’s analysis based in the theory of beam deflections (valid only within the elastic limit of the material, stress must not exceed the yield strength).
What is Euler’s formula used for?
Calculates the critical load (max compressive load a strut can withstand before it becomes unstable and buckles) for a long, slender strut.
Euler’s analysis based in the theory of beam deflections (valid only within the elastic limit of the material, stress must not exceed the yield strength).
How is the bending moment calculated in a cantilever beam with a compressive end load?
M(x)= -P(δ-y)
P- load
δ- deflection
y- distance from neutral axis.
What is the equation of flexure for a beam
P(d^2y/dx^2)= EI(d^4y/dx^4)
What is the significance of parameter λ in Euler’s formula?
λ= sqrt(P/EI) dimensionless parameter that relates the applied load, material properties, cross- sectional area.
General solution to the differential equation of flexure for a strut?
y(x): A1sin(λx) + A2cos(λx) +δ
Critical load for a strut according to Euler’s formula?
Pcritical= π^2EI/(4L^2)
What are the three possible cases for the end load P
- P< Pcr: strut is STABLE. Small deflection will return to 0.
- P= Pcr: state of neutral stability, small deflection maintained without force.
- P> Pcr: strut is unstable, small deflection will increase without limit.
Why is the weakest axis always considered
It is the axis along which the member is most likely to fail. Bending moment (the internal force) is greatest at the weakest axis. Safety efficiency and cost.
What is the moment of inertia
Physical quantity that measures an object’s resistance to changes in its rotational motion. ‘How difficult it is to accelerate a rotating object’.
Depends on the distribution of mass within the object and axis of rotation.
I= mr^2, m- mass of the point, r- distance of the point from axis of rotation.
