Stress analyses Assignmet

Stress Analyses Assignment
Student’s Name
Institutional Affiliation
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.