Civil Engineering Reference
In-Depth Information
where
α
=
P
/
P
CR
and
P
CR
=
π
2
EI
/
L
2
. Assume that
t
is small compared with
d
so that
the cross-sectional area of the tube is
π
dt
and its second moment of area is
π
d
3
t
/
8
.
P.21.5
In the experimental determination of the buckling loads for 12.5mm diameter,
mild steel, pin-ended columns, two of the values obtained were:
(i) length 500mm, load 9800N,
(ii) length 200mm, load 26 400N.
(a) Determine whether either of these values conforms to the Euler theory for
buckling load.
(b) Assuming that both values are in agreement with the Rankine formula, find the
constants
σ
s
and
k
. Take
E
=200 000N/mm
2
.
Ans.
(a) (i) conforms with Euler theory.
(b)
σ
s
=317N/mm
2
10
−
4
.
k
=1.16
×
P.21.6
A tubular column has an effective length of 2.5m and is to be designed to carry
a safe load of 300 kN. Assuming an approximate ratio of thickness to external diameter
of 1/16, determine a practical diameter and thickness using the Rankine formula with
σ
s
=330N/mm
2
and
k
=1/7500. Use a safety factor of 3.
Ans
. Diameter =128mm thickness=8mm.
P.21.7
A mild steel pin-ended column is 2.5m long and has the cross section shown
in Fig. P.21.7. If the yield stress in compression of mild steel is 300N/mm
2
, determine
the maximum load the column can withstand using the Robertson formula. Compare
this value with that predicted by the Euler theory.
Ans.
576 kN,
P
(Robertson)/
P
(Euler) =0.62.
8mm
6mm
184 mm
8mm
130 mm
F
IGURE
P.21.7
