# Stress analyses Assignmet

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Question 1

Question 1 a

The radius of curvature if an airplane is a function of the airlift and the torque

The gradient is a function of the wing moment of area.

The moment of area is given by product of area and square of radius of curvature (Mason, 2008).

0.209*60.16 m = X^2 * 40cmx 40cm

X = 8.86 m

Precision = Accuracy of the radius of curvature

Upper limit = (0.2095*60.16/40cm*40cm) = 8.9M

Lower limit = (0.2085*60.16 m/ (40cm*cm) = 8.84M

Precision = (8.89+8.84)/2 = 1.31m

(8.86- 8.85) = 0.01M

Question 1 b

The thickness of wing = Drawing thickness * scale of the drawing

Use of similarity can calculate the scale of drawing from the photo = Acual measurementdrawing measurement= 8.86m 0.156mm=56.52Thickness of wing = 56.52*15mm = 0.847M

Question 1 c

Maximum strain = original value of area-stressed areaoriginal area= StressModulus of elasticityStrain = 8.85×0.846-8.85×0.8528.85×0.846=0.003Question 1 d

Calculate the maximum compressive stress = strain * Modulus of elasticity = 0.03*578mpa= 17.34 MpaFactor safety = 560/17.34 =32.29

Question 2

Calculate the location of the centroid

Centroid = YC =b1-2tb1*b1=75mmCentroid = zC =b2-2tb2*b2=45mm (b)

Determine the values of Iz, Iy, and Izy

Moment of area = area *distance*distance

IzIyIzy150*150*12^2 =0.324m^4 12^3*150 = 0. 259M^4 3.24+2.59 =0. 583m^4

(c)

IminI max

149.5*149.5*11.95^2 =0.32m^4 150.5*150.5*12.5^2 = 0.328m^4

(d)

Question 3: Unsymmetrical bending

Imax = 150*12*75^2 = 1.0125 x10^-5v m^4

Orientation of Imax = sin^-1(75/100) = 48.59 degrees

Orientation of the neutral axis = sin^-1(75/100) = 48.59 degrees

(b)

Highest magnitude of stress = ii

Lowest magnitude of stress= i (c)

Calculate the value of the stress at the point ii

Stress = force *Area = 578kN*150*100 = 8.67KPa (compressive)

Question 4: Shear stress in beams

Determine the shear stress = QVIBWhere q is the sectional moment of area

V is the shear force

I is the moment of area and B is the breadth

Point iii iii iv

Shear stress(mpa) 23 78 34 60

(b)

Key values = 23, 78, 34 and 60 mpa(c)

Shear centre = F1h-F2b = 120*40 – 120*35= 600mm

Reference

Mason, W. E., & Herrmann, L. R. (2008). Elastic shear analysis of general prismatic beams. Journal of the Engineering Mechanics Division, 94(4), 965-986.

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