# Civil Engineering - UPSC Civil Service Exam Questions - Discussion

Discussion Forum : UPSC Civil Service Exam Questions - Section 1 (Q.No. 7)

7.

A short column of external diameter

*D*and internal diameter*d*, is subjected to a load*W*, with an eccentricity '*e*', causing zero stress at an extreme fibre. Then the value of '*e*' must beDiscussion:

12 comments Page 1 of 2.
Vikas said:
4 years ago

Thanks, @Ashwani.

(1)

Saqib khattak said:
4 years ago

As we know the formula for Z for ext and int dia is Z= 3.14(D^4-d^4)/32D and we also know that (D^4-d^4)= (D^2-d^2)(D^2+d^2) and we also know the area A= (3.14(D^2-d^2))/4

e=Z/A.

e=(3.14(D^4-d^4)/32D)/(3.14(D^2-d^2))/4.

Hence e will comes after solving.

e= (D^2+d^2)/8D.

e=Z/A.

e=(3.14(D^4-d^4)/32D)/(3.14(D^2-d^2))/4.

Hence e will comes after solving.

e= (D^2+d^2)/8D.

Yempee said:
4 years ago

Thanks @Ashwani Bhandari.

PRAMOD KUMAR said:
5 years ago

@AFRID:

Z=I/y I= (π*D^4)/64 y=D/2 so Z = (π*D^3)/32 .

But as D-d cannot cancel out by D so the term remains same and only 64 cancelled out by 2 hence it is 32.

Z=I/y I= (π*D^4)/64 y=D/2 so Z = (π*D^3)/32 .

But as D-d cannot cancel out by D so the term remains same and only 64 cancelled out by 2 hence it is 32.

Ashwani bhandari said:
5 years ago

We know that e = (Z/A).

Section modulus for circular column Z = πx(D4-d4)÷(32D),

Area A= πx(D2-d2)÷4.

We know the formula of;

(D4-d4) is (D2+d2)( D2-d2),

Then e = Z ÷ A,

We get;

e = (D2+d2)/(8D).

Section modulus for circular column Z = πx(D4-d4)÷(32D),

Area A= πx(D2-d2)÷4.

We know the formula of;

(D4-d4) is (D2+d2)( D2-d2),

Then e = Z ÷ A,

We get;

e = (D2+d2)/(8D).

Afrid said:
5 years ago

How come (32*D)?

Kavya said:
6 years ago

But here Z = (3.14*(D^4-d^4))/16D?

Chhaya said:
6 years ago

Z= (3.14* (D^4 - d^4))/32 D.

A = (3.14 * (D^2 - d^2))/4.

e= (D^2 + d^2)/8 D.

A = (3.14 * (D^2 - d^2))/4.

e= (D^2 + d^2)/8 D.

Asaithambi said:
7 years ago

σ(min) = 0 = (p/A) - (p.e/z),

e = z/A,

z = (3.14 * (D^2 - d^2))/(32 * D),

A = (3.14 * (D^2 - d^2),

σ(min)=(D^2 + d^2)/8D.

e = z/A,

z = (3.14 * (D^2 - d^2))/(32 * D),

A = (3.14 * (D^2 - d^2),

σ(min)=(D^2 + d^2)/8D.

Vikas Niswade said:
7 years ago

Please provide the explanation if anyone can.

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