Question

The cantilevered beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection on the centerline of the beam is given by the following equation.

Y =-wx^2/24EI(x^2-4Lx + 6L^2)

where

y = deflection at a given x location (m)

w = Distributed load (N/m)

E = modulus of elasticity (N/m^2)

I = second moment of area (m^4)

x = distant from the support as shown (x)

L = length of the beam (m)

Generally, deflection can be calculated by taking the double integral of the Bending Moment Equation, M(x) divided by EI (Young's Modulus x Moment of Inertia).

Deflection: Displacement

Problem 14.12

Using Excel, plot the deflection of a beam whose length (L) is 5m with the modulus of elasticity of

E = 200GPa and I = 99.1 *10^6 mm^4. The beam is designed to carry a load of 10,000 Nm. What

is the maximum deflection of the beam ?

WL^4/30EI =

W =10000Nm

L = 5m

E = 200GPa

I = 66.1*10^6mm^4

WL^4/30EI =

{[10000Nm(5^4)]/[30(200GPa)(99.1*10^6mm^4)]}

1.05*10^-6 Nm^5/GPa mm^4

Answer 1

In Excel sheet, column A takes for distance, ie A1 and x  from 0 to 5 ie from A2 to A27

Column B shows the deflection, Y (in meter,m) for every x from B2 to B27. The formulae for deflection can be substituted in B2 as " =(-(10000*A2^2)/(24*(200*10^9)*(99.1*10^6*10^-12)))*((A2^2)-(4*5*A2)+(6*5^2)) " as per the equation for Y given in the question as shown in figure and then drag cursur to down till B27 will give you the answer. Plot using recommended chart options from insert as shown in figure. From the plot it is clear that the maximum deflection is at x=5 and Y= -0.039417255 (B27).