The deflection function of a one-way plate with span L built-in at both ends is:
a) Check whether the deflection function fulfills the boundary conditions.
b) Using the differential equation of the plate, calculate the distributed load.
c) Calculate the deflection at mid-span.
d) Calculate the moments Mx and My at the x = 0 edge (Poisson’s ration is ν).
Solve Problem
Constant load, p [kN/m2]= Midspan deflection, w(L/2)= Moment, Mx(0)= Moment, My(0)=Solve
Check formula
Check formula
Check formula
Do you need help?
Steps
Problem a) Step 1. Check boundary conditions at built-in edge, x = 0. The deflection function fulfills the boundary conditions at x = 0. Step 2. Check boundary conditions at built-in edge, x = L. The deflection function fulfills the boundary conditions at x = L. Problem b) Step 1. Give the load function deriving the fourth derivative of the deflection. Higher order derivatives of the deflection function are: The load function obtained from by the DE of the one-way slab is constant: When the unit of the length is [m] and the stiffness of the slab is given in [kNm2/m], then the load is in [kN/m2] while the deflection is in [m]. Problem c) Step 1. Calculate midspan deflection at x = L/2. Problem d) Step 1. Give the moments from the second derivatives of the deflection function. Note that the derivatives of the deflection function with respect to to y is zero.Step by step
Show boundary conditions
Show boundary conditions
Show load
Show deflection
Show moments
Results
Problem a) The deflection function fulfills the boundary conditions at x = 0: The deflection function fulfills the boundary conditions at x = L: Problem b) Higher order derivatives of the deflection function are: The load function obtained from by the DE of the one-way slab is constant: When the unit of the length is [m] and the stiffness of the slab is given in [kNm2/m], then the load is in [kN/m2] while the deflection is in [m]. Problem c) Midspan deflection at x = L/2 is Problem d) The moments are given by the second derivatives of the deflection function. Note that the derivatives of the deflection function with respect to y is zero.Worked out solution