Design equation, strength, design stress, modes of failure, failure criterion

1. Design Equation
V K Jadon
V K Jadon, Professor, Mechanical Engineering

2. 𝜎 =
𝐹
𝐴
𝜎 𝑚𝑎𝑥 =
10000
(15)(15)
= 14.4 𝑀𝑃𝑎
Find maximum stress induced in the
member if load is 10 kN and side is
15 mm.
Find required cross-section of the
member loaded with 10 kN load, if
the maximum permissible stress
(design stress) is 100 MPa.
𝜎 𝑚𝑎𝑥 max induced stress F is external load
Find required cross-section of the
member if maximum elongation
( 𝛿 𝑚𝑎𝑥 ) in the member is not to
exceed 0.001 mm.
𝑏 =
𝐹
𝜎 𝑑
𝜎 𝑑 is design stress
F is external load
= 10 𝑚𝑚
𝛿 =
𝐹𝐿
𝐸𝐴
𝑏 =
𝐹𝐿
𝐸𝛿 𝑑
𝐸 = 210 𝐺𝑃𝑎
𝐿 = 1000 𝑚𝑚
F is external load
= 6.9 𝑚𝑚
Design Equation
=
10000
100
=
10000
210000(0.01)
𝐹
𝑏2
= 𝜎 𝑑
Maximum induced stress at any point in a loaded machine member <= Design Stress
𝐹𝐿
𝐸𝐴
= 𝛿 𝑑
Maximum deformation (axial or twist) at any point in a loaded machine member <= Maximum permissible value
Design equations are to be developed at a point
Design Stress =
𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦Static Load

3. Design Equation
For LHS of design equation, we have to identify the point
where induced stresses are maximum.
Let us consider a section through point A.
 The effect of 500 N load (point D) is to twist (x-y) and bend
(y-z) in addition to transverse load.
 The effect of 600 N load (point D) is to bend (x-z plane and
y-z plane) in addition to axial load along y-axis.
 The effect of 400 N load (point D) is to twist (x-y) and bend
(x-z) in addition to transverse load along x axis.
 So on……
Maximum induced stress at any point in a loaded machine member <= Design Stress

4. Design Equation
𝑭 𝑭
Design of the fork bolt

5. Design Equation
Design of the fulcrum pin

6. Case-C: We need to know the support reactions to obtain the load on the
member supporting the main member. The evaluation of support reactions
is based on the following:
 Equations of Static Equilibrium
 Free body diagram
Case-A: We need to know the effect of the
load at point of interest to find stresses (LHS)
due to load acting at some other point.
Design Equation
Case-B: We need to know how the load transfer takes place in an assembly
from one member to another member.
A single load may for induce multiple stresses (crushing and shear in bolt).
Hence, there would be two mode of failure.

7. References