40-mmRod ABC consists of two cylindrical portions AB and BC; it is made of a mildsteel that is assumed to be elastoplastic with E = 200 GPa and oy = 250 MPa.A force P is applied to the rod and then removed to give it a permanent set8, = 2 mm. Determine the maximum value of the force P and the maximumamount 8, by which the rod should be stretched to give it the desired permanent1.2 mdiameterB30-mm0,8 mdiameterset.P

Given data: Modulus of elasticity for mild steel rod, E=200 GPa Yielding strength for the rod is,…

Answered: 40-mm Rod ABC consists of two…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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40-mm
Rod ABC consists of two cylindrical portions AB and BC; it is made of a mild
steel that is assumed to be elastoplastic with E = 200 GPa and oy = 250 MPa.
A force P is applied to the rod and then removed to give it a permanent set
8, = 2 mm. Determine the maximum value of the force P and the maximum
amount 8, by which the rod should be stretched to give it the desired permanent
1.2 m
diameter
B
30-mm
0,8 m
diameter
set.
P

Expert Solution

Step 1

Given data:

Modulus of elasticity for mild steel rod, $E = 200 GPa$
Yielding strength for the rod is, $σ_{y} = 250 MPa$
Permanent set due to force $P$ , $δ_{p} = 2 mm$
Diameter of rod AB, $D_{A B} = 30 mm$
Length of rod AB, $L_{A B} = 0.8 m$
Diameter of rod BC, $D_{B C} = 40 mm$
Length of rod BC, $L_{B C} = 1.2 m$

For maximum value of force $P_{m a x}$ ,

We know that from definition of yielding strength,

$\begin{array}{rcl} σ_{y} & = & \frac{P_{m a x}}{A_{m i n}} \\ P_{m a x} & = & σ_{y} \cdot A_{m i n} \\ = & (250 MPa) \times (π \frac{D_{A B}^{2}}{4}) \\ = & (250 MPa \times \frac{10^{6} N / m^{2}}{1 MPa}) \times (π \frac{{(30 mm)}^{2} \times \frac{1 m^{2}}{10^{6} {mm}^{2}}}{4}) \\ = & 176714 N \\ = & 176.7 kN \end{array}$

Thus, maximum value of force is $176.7 kN$ .

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