#1 Shape Factor For the extruded aluminum cross-section below, what would the sh

Question

#1 Shape Factor For the extruded aluminum cross-section below, what would the shape factor be? What would be the dimensions for a square cross-section of solid material of same weight as extruded cross-section? What would the cross-section need to be in order to have the same bending benefit if you were to have a solid square cross-section? How much (%) heavier would it be than the extruded cross- section? a) b) c) If you were to make a square hollow cross-section of same weight as the extruded cross-section shown below with web thickness equal to 1/8 the total outer square width, what would the shape factor be? HFS (Standard Type NFS (Economy Type) 20 12 600SA-TS Aluminum Mass/length 0.5 kg/m sectional area = 183 mm2 y-0. 742E4 mm

Explanation / Answer

(a) Shape factor of any cross-section for elastic bending,

?eB = (Bending stiffness of a section) / (Bending stiffness of a circular section of same area and material)

= EI / EI0; where E = Young’s modulus and I = second moment of area of a section

= I / I0

Now, I0 = (?*D4)/64; where D = diameter of circular cross-section

=> I0 = (?*D4)/64 = (A2/4?); where A = cross-sectional area

So, ?eB = I / (A2/4?) = Ix / (A2/4?) = 7420 / (1832/4?) = 2.78

(b) Mass = 0.5 kg/m = (0.5/1000) kg/ mm = 0.0005 kg/ mm

Density = 0.0005/183 kg/ mm3

Let a square cross-section has each side = X mm

For 1 mm length, volume of the square = X2 * 1 = X2

So, mass of the square block = X2 * density = X2 * (0.0005/183)

Now, X2 * (0.0005/183) = 0.0005 => X = 13.53 mm

(c) Let the hollow square cross-section has outer width = b and web thickness = t

I for the hollow square cross-section = 2*b3*t/3 = 2*b3*(b/8)/3 = b4/12

Area of the hollow square cross-section = b2 – (b – b/4)2 = 7 b2/16

Since the weight of hollow square and given section are same,

(7 b2/16) * (0.0005/183) = 0.0005 => b = 20.45

I = b4/12 = (20.45)4/12 = 14574.44 mm4

Area = 7 b2/16 = 7*20.452/16 = 182.96

Hence, shape factor = I / (A2/4?) = 14574.44 / (182.962/4?) = 5.47

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