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Calculating the Second Moment of Area

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It is necessary to design a square-section composite bar that will withstand an applied load without deflecting more than a specified amount.The design specification for the bar, including its dimensions and loading criteria, is given below.

Using the formula below, calculate the second moment of area of the bar and use this to estimate the modulus of a composite material that will just meet the design specification.

The composite is made up of polymer fibres all aligned along the length of the bar combined with an epoxy matrix and each has the properties listed below. Estimate the minimum volume fraction of fibres that the composite must contain to meet the design specification.

Length: l= 0.5m
Thickness: a=10mm
Max deflection=2mm
Applied load: F=5kg at centre of the bar
Acceleration due to gravity:g =9.8m s(to power -2)

Second moment of area of a square section of side a: I=a(to power of 4)/12

Max deflection of beam of material modulus E=Fl(to power of 3)/48EI

Modulus of fibres: E fibre= 125GN m(to power -2)

Modulus of matrix: E epoxy= 3.5GN m(to power -2)

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Let's denote with (E) the necessary modulus for the composite beam so that it withstands the load (F) getting the maximum acceptable deflection (derivative_max) .

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