Buckling of Struts - MKM
Buckling of Struts - MKM
Buckling of Struts - MKM
BUCKLING OF STRUTS
Theory
A strut is a long thin compression member. It may collapse under a compressive
load by buckling and bowing out as shown in Fig.1. The diagram shows the member
with its length horizontal but it is just as likely to be vertical. It is drawn this way so that
the x-y coordinates are in the normal position at the left end. X measures the distance
along the length and Y is the deflection.
Now consider a vertical strut with weights causing the compression. If the load is
critical; the strut will start to deflect. As the distance y increases so will the bending
moment. This in turn makes it deflects even further. This is a run-away or unstable
condition and the strut keeps on bending and fails. A strut is an unstable structure as
collapse is sudden and without warning.
Description
The Buckling of Struts experiment consists of a back plate with a load cell at one end
and a device to load the struts at the top. There are five aluminium alloy struts included
in a holder on the back plate. The struts provided have an l/r ratio of between 520 and
870, which are impractical in real terms but have been designed to show the buckling
load (in accordance with Euler) and the deflected shape of the strut as clearly as
possible. Printed on the equipment are a number of equations and pieces of information
that you will find useful while using the equipment shown in Figures 3 and 4.
In this experiment we will load struts until they buckle investigating the effect of the
length of the strut. To predict the buckling load we will use the Euler buckling formulae.
Critical to the use of the Euler formulae is the slenderness ratio, which is the ratio of
the length of the strut to its radius of gyration (l/r). The Euler formulae become
inaccurate for struts with a Slenderness ratio of less than 125 and this should be taken
into account in any design work. The struts provided have an l/r ratio of between 520
and 870 to show clearly the buckling load and the deflected shape of the struts. In
practice struts with an l/r ratio of more than 200 are of little use in real structures.
Where:
Pe = Euler buckling load (N);
E = Youngs modulus (Nm2);
I = Second moment of area (m4);
L = Length of strut (m).
By referring to Figures 5A, 5B and 5C fit the struts in position corresponding to the end
conditions. Then calculate the cross sectional area and moment of inertia by measuring
the dimensions of the struts. Then follow the procedure for loading and calculate the
buckling load on the struts as given below.
Adjust the position of the sliding crosshead to accept the strut using the thumbnuts to
lock off the slider. Ensure that there is the maximum amount of travel available on the
hand wheel thread to compress the strut. Finally tighten the locking screws. Carefully
back off the hand wheel so that the strut is resting in the notch but not transmitting any
load; rezero the force meter using the front panel control.
Carefully start to load the strut. If the strut begins to buckle to the left, flick the strut to
the right and vice versa (this reduces any errors associated with the straightness of the
strut). Turn the hand wheel until there is no further increase in load (the load may peak
and then drop as it settles into the notches).
Record the final results in corresponding tables (Table1,2 & 3) under buckling load.
Repeat with strut numbers 2, 3, 4 and 5 adjusting the crosshead as required to fit the
strut. Take more care with the longer struts, as the difference between the buckling load
and the load needed to obtain plastic deformation is quite small. Try loading each strut
several times until a consistent result for each strut is achieved.
Length (mm)
1
2
3
4
5
320
370
420
470
520
Pe
Pe (T)
1/L2
Strut ID
Length (mm)
1
2
3
4
5
300
350
400
450
500
Pe (T)
1/L2
Strut ID
Length (mm)
1
2
3
4
5
280
330
380
430
480
Pe (T)
1/L2