Mechanical Engineering Principles

16 MECHANICAL ENGINEERING PRINCIPLES

Now try the following exercise

Exercise 5 Further problems on

compound bars

1. Two layers of carbon fibre are stuck to
   each other, so that their fibres lie at 90°
   to each other, as shown in Figure 1.15.
   If a tensile force of 1 kN were applied to
   this two-layer compound bar, determine
   the stresses in each. For layer 1,E 1 =
   300 GPa andA 1 =10 mm^2 ; for layer 2,
   E 2 =50 GPa andA 2 =A 1 =10 mm^2.
   [σ 1 = 85 .71 MPa,σ 2 = 14 .28 MPa]

Layer 1

Layer 2

PP

Figure 1.15 Carbon fibre layers

2. If the compound bar of Problem 1 were
   subjected to a temperature rise of 25°C,
   what would the resulting stresses be?
   Assume the coefficients of linear expan-
   sion are, for layer 1,α 1 = 5 × 10 −^6 /°C,
   and for layer 2,α 2 = 0. 5 × 10 −^6 /°C.
   [σ 1 = 80 .89 MPa,σ 2 = 19 .10 MPa]

Exercise 6 Short answer questions on the

effects of forces on materials

1. Name three types of mechanical force
   that can act on a body.


2. What is a tensile force? Name two prac-
   tical examples of such a force.


3. What is a compressive force? Name two
   practical examples of such a force.


4. Define a shear force and name two prac-
   tical examples of such a force.


5. Define elasticity and state two examples
   of elastic materials.


6. Define plasticity and state two examples
   of plastic materials.


7. Define the limit of proportionality.


8. State Hooke’s law.
   10. What is the difference between a ductile
   and a brittle material?
   11. Define stress. What is the symbol used
   for (a) a tensile stress (b) a shear stress?
   12. Strain is the ratio

......

......

13. The ratio

stress

strain

is called......

14. State the units of (a) stress (b) strain
    (c) Young’s modulus of elasticity


15. Stiffness is the ratio

......

......

16. Sketch on the same axes a typical
    load/extension graph for a ductile and a
    brittle material.


17. Define (a) ductility (b) brittleness
    (c) malleability


18. Define rigidity modulus.


19. The new lengthL 2 of a bar of length
    L 1 , of coefficient of linear expansionα,
    when subjected to a temperature riseT
    is:L 2 =......


20. The thermal strainεdue to a temperature
    riseTin material of coefficient of linear
    expansionαis given by:ε=......

Exercise 7 Multi-choice questions on the

effects of forces on materials

(Answers on page 284)

1. The unit of strain is:
   (a) pascals (b) metres
   (c) dimension-less (d) newtons


2. The unit of stiffness is:
   (a) newtons
   (b) pascals
   (c) newtons per metre
   (d) dimension-less


3. The unit of Young’s modulus of elastic-
   ity is:

(a) Pascals (b) metres

(c) dimension-less (d) newtons

4. A wire is stretched 3 mm by a force of
   150 N. Assuming the elastic limit is not