1. Load, Stress and Failure

2. Design Basic Selection
 Mechanism
Depends on the purposes of the machine
 Materials
Depends on the shape of the part, loading and operation
(corrosion & wear resistance … etc)
 Stresses
Requires a working knowledge of the materials
 Cost
Is always an important factor

3. Failure of machine parts
There are two types:
Functional failure
Fracture failure

4. Failure of machine parts
 Functional failure
e.g. Excessive deflection of shaft
Noise, decrease in efficiency, increase in
heat generation
Functional failure could be as a result of:
Deformation
Wear
corrosion

5. Fracture failure
 Excessive stress
–Tensile
–Shear
–Combined stress
–Fatigue
–Crack
–Stress concentration
Excessive stress results of high load
or low allowable material properties
or dimensions

6. Load:
A component subjected to a single
load implies:
• A transverse force in the case of a
beam component,
• A longitudinal compressive force in
a column,
• A torque in the case of a shaft,
• A pressure in a fluid containment
vessel, and so on

7. Expressions of the load:
 The actual load, extrinsic,:
is the load exerted on the component by its
surrounds, and
The maximum load, intrinsic,:
is the largest load that the component can
withstand without failure;
 The maximum load is a property of the
component, a function of its dimensions and
material properties

8. Factor of safety
• Uncertainty about the actual
load.
• Uncertainty about the
maximum allowable load

9. Uncertainty about the actual load
The inherent variability of the load
(e.g. in practice the mass of a "ten tonne truck" will
depend on the load it's carrying),
Static indeterminacy
(when components share the load in proportion to their
elastic responses),
Dynamic (or shock) effects
If a weight W is dropped from a height h onto an elastic
component of stiffness k, , then the peak force in the
component is = dynamic magnification factor (dmf) * W

10. Inherited Variability of Actual Load
25
Frequency
20
15
10
5
0
900 925 950 975 1000 1025
Actual Load

11. Dynamic magnification factor
 Elementary energy methods give
dmf = [ 1+ ( 1 + 2hk/W)1/2 ]
W
The effective actual load is h
at least twice its nominal or
supposed value
k

12. Uncertainity about the maximum allowable
load
 dimensions differing from their
nominal or expected values
 material strength differing from its
nominal value due in turn to
– variations in material composition
– variation in heat treatment,
– unsuspected flaws

13. Factor of safety (fs)=
Maximum allowable load
Actual load
It follows that :
if fs = 1 then the component is on the point
of failure
if fs < 1 then the component is in a failed
state
if fs > 1 then the component is safe

15. Suggested Safety (design) Factors for Elementary Work
For exceptionally reliable materials used under controllable
1.25 - 1.5 conditions and subjected to loads and stresses that can be
determined with certainty - used where low weight is very important
consideration
1.5 - 2 For well-known materials under reasonably constant environmental
conditions, subjected to loads and stresses that can be determined
readily.
2 - 2.5 For average materials operated in ordinary environments and
subjected to loads and stresses that can be determined.
2.5 - 3 For less tried materials or for brittle materials under average
conditions of environment, load and stress.
3-4 For untried materials used under average conditions of
environment, load and stress.
3-4 Should also be used with better-known materials that are to be used
in uncertain environments or subject to uncertain stresses.
Repeated loads : the factors established in items 1 to 6 are acceptable but must
be applied to the endurance limit rather than to the yield strength of the
material.

16. Impact forces : the factors given in items 3 to 6 are
acceptable, but an impact factor (the above dynamic
magnification factor) should be included.
Brittle materials : where the ultimate strength is used
as the theoretical maximum, the factors presented in
items 1 to 6 should be approximately doubled.
Where higher factors might appear desirable, a more
thorough analysis of the problem should be
undertaken before deciding on their use.

17. Important points :
Loads not known for certainty :
Increase factor of safety
e.g for shock loads; obtain a realistic dmf .. search
internet, other sources
Employ reasonable accurate
mathematical models rather than using
simple models
Design factors are increased also
when the consequences of failure are
serious
Economic, social, environmental or
political
e.g. the headwaters of a remote River, doubled the
size of every motor predicted

18. Stress concentration
Sudden change of cross-section
F F
Presence of a hole
Hole
F F

19. Stress concentration on gears
Low
stress
High
stress

20. Stress concentration near a hole
So
o
3So
So
1 2 3 4d
d

21. Hole
F F

Stresses are low where the streamlines are widely
spaced.
 Stresses are high where the streamlines are
bunched together due to geometric shape
variations
 The more sudden these variations, the higher the
local stresses.
 This last is known as stress concentration.
 Geometric irregularities give rise to non-uniform
stresses

22. Estimation of Stress Concentration Factor:
Form factor (K)
S =F/(b - d)h
3
F F
factor K
b d
2.5
o
h
Form stress
2
1.5
1
0 0.2 0.4 0.6 0.8
Ratio d/b
Form stress factor due to hole in
narrow plate

23. The stress concentration factor (K’).
K ' = 1 + q(K -1)
 Where q: index of sensitivity of the material
Static loads: Impact load
Material Index of Material Index of
sensitivity sensitivity
Ductile material 0 Ductile and very soft 0.4
material
Brittle material, hardened 0.1
steel Ductile material 0.61
Very brittle material, 0.2 Brittle material, hardened 1
quenched steel steel
Cast iron 0.5
Cast iron 0

24. For repeated loads
Index of sensitivity
Material Heat treated Heat treated
Annealed
and drawn at and drawn at
or soft
12000 F 9000 F
Armco iron, 0.02% C 0.15 0.20 ….. …..
Carbon steel
0.05 – 0.10 ….. …..
0.10% C
0.10 ….. …..
0.20% C (also cast steel)
0.18 0.35 0.45
0.30% C
0.26 0.40 0.50
0.50% C
….. 0.45 0.57
0.85% C
Spring steel, 0.56% C, 2.3 Si rolled …. 0.38 ….
SAE 3140, 0.37 C, 0.6 Cr, 1.3 Ni 0.25 0.45 ….
Cr-Ni steel 0.8 Cr, 3.5 Ni ….. 0.25 …..
Stainless steel, 0.3 C, 8.3 cr, 19.7 Ni 0.16 ….. ……
Cast iron 0 – 0.05 ….. …..
Copper, electrolite 0.07 ….. …..
Duraluminum 0.05 – 0.13 ….. …..

25. Theories of Failures
 Failureof a tensile member occurs
when the stress reaches the stress
limit
 How can we correlate the triaxial stress
state in a component –
 Material strength(s) is measured in
uniaxial tests

26. Theories of failure
1. Maximum Normal Stress theory (Rankine):
S1= Sy
Hold well for brittle materials
2. Maximum strain Theory (Saint Venant ):
2 2
0 . 35 0 . 65 S 4S s Se
It holds well for ductile materials. It is the best of five
3. Maximum Shear Stress Theory (Guest-Tresca):
½(S1 – S2) = ½ Sy
Sy= S1-S2
Holds well for ductile materials

27. Theories of failure
1. Shear energy theory (Von Mises):
2 2
S 3S s
Se
Hold well for ductile materials

28. Thank You