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 3 of 4.
Anubhav Srivastav said:
9 years ago
Slenderness ratio = le/r(min).
le = 300 ,r(min) = (I/A)^1/2
Ixx = a^4/12= 25^4/12 = 32552 cm^4,
A = 25^2= 625 cm^2.
Rmin = (32552 cm^4/ 625 cm^2)1/2 = 7.21 cm.
Slenderness ratio = 300/7.21= 41.6cm = 416mm.
le = 300 ,r(min) = (I/A)^1/2
Ixx = a^4/12= 25^4/12 = 32552 cm^4,
A = 25^2= 625 cm^2.
Rmin = (32552 cm^4/ 625 cm^2)1/2 = 7.21 cm.
Slenderness ratio = 300/7.21= 41.6cm = 416mm.
Subhankar said:
9 years ago
300 * 2 * √3/2.5 = 415.69.
Ferdieb said:
9 years ago
Slenderness ratio = L/sq.root of (Ix/A).
Ix of cross section of column = BD^3/12 ie. 3.25cm^4.
Area of cross section of column = BD ie. 6.25 cm2.
Thus, 300/sq.root of (3.25/6.25) = 416.025.
Ix of cross section of column = BD^3/12 ie. 3.25cm^4.
Area of cross section of column = BD ie. 6.25 cm2.
Thus, 300/sq.root of (3.25/6.25) = 416.025.
Mohammad amir said:
10 years ago
L/r and eff L/k.
k = square root I/a consider both different formula guys.
k = square root I/a consider both different formula guys.
Raj said:
1 decade ago
All you guys are correct and I want add a point.
Slenderness ratio = Effective length/Maximum radius of gyration.
Thanks.
Slenderness ratio = Effective length/Maximum radius of gyration.
Thanks.
Anil Baral said:
1 decade ago
r = sqrt (I/A).
A = 2.5*2.5.
I = 2.5^/4.
There fore, r = 2.5*sqrt (1/12).
r = 300/2.5*sqrt (1/12).
= 415.69 approx=416.
A = 2.5*2.5.
I = 2.5^/4.
There fore, r = 2.5*sqrt (1/12).
r = 300/2.5*sqrt (1/12).
= 415.69 approx=416.
Xyz said:
1 decade ago
In case of Strength of materials, slenderness ratio is eff length/radius of gyration, while in case of RCC it is eff length/least lateral dimension.
Deepak goel said:
1 decade ago
Its value is wrong because slenderness ratio is l/r means 300/2.5 = 120.
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.
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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