Question

INGE 4019 Introduction to Mechanics of Materials March 6, 2019 A Problem 4, (20 points) An axial centric force of magnitude P 450 kN is applied to the composite block shown by means of a rigid end plate. Knowing that h -10 mm, determine: 1) the normal stress in (a) the brass core, (b) the aluminum plates. (10 pts.) 2) (a) the value of h if the portion of the load carried by the aluminum plates is half the portion of the load carried by the brass core, (b) the total load if the stress in the brass is 80 MPa. (10 pts.) Brass core E 105 GPa) Rigd Aluminum plates E-70 GPa P end plate 300 mm 60 mm 0 mm

Answer 1

1) STEP- I

Strategy The deformation of brass core and aluminum core will be same. The total load will be shared by them. From these two conditions we can find the load shared by each metal and thus the resultant deformation can be calculated. Given data Applied Load: P = 450 kN Modulus of Elasticity of brass: Eb 105 GPa Modulus of Elasticity of Aluminu: Ea 70 GPa Deformation of brass core: Deformation of Aluminum plates: 5, Area of brass core: A-60 mm x 40 mm A 2400 x 10-6m2 Area of Alumin core: A 2 x 60 mmx 10 mm A 1200 x 10-6m2

STEP-II

Equations of compatibility From Deformation of brass core P,L From Deformation of aluminum core PaL

STEP-III

Strain from second Equation of compatibility (450 x 103 N) (F0x 10 Pa) (1200 x 0+ (105 x 10P Pa) (2400 10- 1.33929 x 10-3

STEP-IV

Part (a): Brass Core stress o, = (105 × 10°) (1.33929 × 10-3) Ơb 1.40625 x 108 Pa Part (b): Aluminum plates stress σ,-(70 x 10°) (1.33929 x 10-3) -9.3750 107 Pa

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STEP-I

2) a)

from problem Satment Pa

STEP-II 2) b)

-b A-b