Civil Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 1 (Q.No. 23)
23.
The slenderness ratio of a vertical column of a square cross-section of 2.5 cm sides and 300 cm length, is
Discussion:
33 comments Page 1 of 4.
Amit said:
5 years ago
We Know that Slenderness Ratio is Equal to Length upon Radius of Gyration = L/r.
we have a value of L that is given in question 300.
So, now we need to calculate the value of r that is equal to under root I/A means r= under root I/A.
I Means Moment of Inertia, here for Square Section that is equal to a^4/12 and for A= a^4.
Now, you will get the answer 416.
Thank You.
we have a value of L that is given in question 300.
So, now we need to calculate the value of r that is equal to under root I/A means r= under root I/A.
I Means Moment of Inertia, here for Square Section that is equal to a^4/12 and for A= a^4.
Now, you will get the answer 416.
Thank You.
(2)
Bikash Kabiraj said:
8 years ago
Slenderness ratio = effective length/radius of gyration.
Radius of gyration = under root of i/a,
i = moment of inertia and a =cross sectionl area. i=2.5^4/12= and a = 2.5^2.
So radius of gyration = 0.721.
Soslenderness ratio=300/0.721 = 416.088.
Radius of gyration = under root of i/a,
i = moment of inertia and a =cross sectionl area. i=2.5^4/12= and a = 2.5^2.
So radius of gyration = 0.721.
Soslenderness ratio=300/0.721 = 416.088.
Piyush singh said:
1 decade ago
Slenderness Ratio (lemma ) = L(eff) / R(min).
Rmin = under root of ( Imin / area ).
Imin = (b*d^3) / 12.
Area = (b*d).
(b=d).
Imin / Area = b^2 / 12.
Rmin = under root of (b*b / 12).
Rmin = 0.2886 b^ 2.
Slender ness Ratio = (Leff / R min).
= (300 / ( 0.886*2.5).
= 415.96 = 416.
Rmin = under root of ( Imin / area ).
Imin = (b*d^3) / 12.
Area = (b*d).
(b=d).
Imin / Area = b^2 / 12.
Rmin = under root of (b*b / 12).
Rmin = 0.2886 b^ 2.
Slender ness Ratio = (Leff / R min).
= (300 / ( 0.886*2.5).
= 415.96 = 416.
DEVARAJ said:
6 years ago
Slenderness ratio = effective length / radius of gyration.
Radius of gyration = Sqrt(moment of inertia/area of Cross section).
Moment of inertia (I) = b^4/12 (column is a square Cross section).
Assume given length as effective length put All values in the above equations. You will get answer.
Radius of gyration = Sqrt(moment of inertia/area of Cross section).
Moment of inertia (I) = b^4/12 (column is a square Cross section).
Assume given length as effective length put All values in the above equations. You will get answer.
(1)
Bharat meena said:
9 years ago
Slenderness ratio=le/k.
K=I/A saqur Root
I =bd^3/12.
A =b * d.
I = 2.5 * 2.5^3/12 = 3.255cm^4.
A =2.5*2.5= 6.25cm.
k^2=3.255÷ 6.25 = 0.721.
Slendernes ratio=300÷0.721 = 416.
K=I/A saqur Root
I =bd^3/12.
A =b * d.
I = 2.5 * 2.5^3/12 = 3.255cm^4.
A =2.5*2.5= 6.25cm.
k^2=3.255÷ 6.25 = 0.721.
Slendernes ratio=300÷0.721 = 416.
Ramana panchadi said:
8 years ago
Slenderness ratio=L effective/Kmin.
K=radius of gyration;K=sq root of i/a;i=moment of intertia @ a=cross sectional area.
k=solid circle=d/4,
K=square=a/2 root 3,
Sol:- K=2.5/2 root 3 =0.7122.
Slenderness ratio=300/0.71222=415.69.
K=radius of gyration;K=sq root of i/a;i=moment of intertia @ a=cross sectional area.
k=solid circle=d/4,
K=square=a/2 root 3,
Sol:- K=2.5/2 root 3 =0.7122.
Slenderness ratio=300/0.71222=415.69.
Pradhyumna said:
1 decade ago
Dear @Kaushal, clear the definition first.
Slenderness ratio = Unsupported length of column/minimum radius of gyration of cross-section.
Hence, SR = 300/rad. of gyration.
= 300/ sq.root of ((2.5^4/(12*2.5^2))).
= 415.692.
= 416.
Slenderness ratio = Unsupported length of column/minimum radius of gyration of cross-section.
Hence, SR = 300/rad. of gyration.
= 300/ sq.root of ((2.5^4/(12*2.5^2))).
= 415.692.
= 416.
Yamiiiii said:
7 years ago
S.R=Equivalent length of column or unsupported length/least radius of gyration
=Le/k,
=Le/√(I/A).
√[I/A] =root[(2.5/12)*(1/2.5)],
=0.72168783654321698610321.
S.R=300/0.72168783654321698610321.
S.R=415.6921938=415. 69=416.
=Le/k,
=Le/√(I/A).
√[I/A] =root[(2.5/12)*(1/2.5)],
=0.72168783654321698610321.
S.R=300/0.72168783654321698610321.
S.R=415.6921938=415. 69=416.
Kaushal said:
1 decade ago
According to me, Slenderness ratio is kl/b. where k is length factor, l is the length of column and b is the width.
Let us suppose k = 1 (pin jointed both sides).
Slenderness ratio = 1*300/2.5 = 120.
How could answer be 416?
Let us suppose k = 1 (pin jointed both sides).
Slenderness ratio = 1*300/2.5 = 120.
How could answer be 416?
Pawan kumar said:
1 decade ago
You are right @Pradhyumna.
Slenderness ratio = l/k = 300/0.7217= 415.692=416.
K = radius of gyration = root under(I/A) = under root 0.52.
I/A = (moment of inertia/area) = 2.5*2.5*2.5*2.5/12)/(2.5*2.5)=0.52.
Slenderness ratio = l/k = 300/0.7217= 415.692=416.
K = radius of gyration = root under(I/A) = under root 0.52.
I/A = (moment of inertia/area) = 2.5*2.5*2.5*2.5/12)/(2.5*2.5)=0.52.
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