Load Deflection Relation (2.4) - Superposition Priciple (2.5) - Edubirdie

University:
McMaster University
Course:
MATLS 2H04 | Introduction to Materials Engineering
Academic year:

2023
Views:

403

Pages:

1
Author:

Sabrina S.

2.4 Pure Bending - Load Deflection Relation ρ = dx/ds α + dα = v'(x - dx) K = 1/p = da/dx ≈ v''(x) εx = -ky = -v''(x)y sometimes group ET = β B is the flexural rigidity M(x) = EIx'' 2nd derivative of the deflection bending moment Cantilever w applied moment ⇒ integrating twice & applying some boundary conditions gives v(x) = Mx^2 / (2EI) x = distance along a linear beam vmax = v(l) = Ml^2 / (2EI); vmax' = v'(l) = Ml / (EI) unit length Cantilever with distributed load v(x) = ωx^2 / (24EI)(6L^2 - 4Lx + x^2) vmax = v(l) = ωL^4 / (8EI), vmax' = v'(l) = ωL^3 / (6EI) 2.5 Pure Bending Superposition Principle combining 2 individual load relations eg. cantilever beam applied moment + distributed load v = wx^2 / (24EI)(x^2 + 4Lx + 6L^4) + Mx^2 / (2EI)

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