Mechanical Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 3 (Q.No. 8)
8.
A column of length (l) with both ends fixed may be considered as equivalent to a column of length __________ with both ends hinged.
Discussion:
3 comments Page 1 of 1.
Kousik Sarkar said:
5 years ago
The equivalent length for both ends fixed beam(Le) = l/2.
The equivalent length for both ends hinged(Le) = L.
crippling load of column=(pie)^2.E.i/(Le)^2.
now equating both columns.
(π)^2.E.i/(l/2)^2=(π)^2.E.i/(L)^2,
4/l^2=1/L^2.
By cross multiplication
4L^2 = l^2.
sqrt(4L^2) = l.
2L= l.
L = l/2 hence proved.
A column of length l having both ends fixed is equal to a column of length l/2 having on both ends hinged.
The equivalent length for both ends hinged(Le) = L.
crippling load of column=(pie)^2.E.i/(Le)^2.
now equating both columns.
(π)^2.E.i/(l/2)^2=(π)^2.E.i/(L)^2,
4/l^2=1/L^2.
By cross multiplication
4L^2 = l^2.
sqrt(4L^2) = l.
2L= l.
L = l/2 hence proved.
A column of length l having both ends fixed is equal to a column of length l/2 having on both ends hinged.
Abhishek kumar said:
8 years ago
EQUIVALENT LENGTH (Le) for different loading conditions are as follows.
Both end hinged ---- Le= L.
Both end fixed -----Le= L/2.
Critical loading Pcr = (pi * pi * E * I)/(Le * Le).
Now, find length of the column such that the critical load (Pcr) should be same for both the above case, you will get the length of the column for both ends hinged is l/2.
Both end hinged ---- Le= L.
Both end fixed -----Le= L/2.
Critical loading Pcr = (pi * pi * E * I)/(Le * Le).
Now, find length of the column such that the critical load (Pcr) should be same for both the above case, you will get the length of the column for both ends hinged is l/2.
Manila kanika said:
9 years ago
How, can anyone explain this?
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