Column Buckling Laboratory: Worksheet - Desklib

Material Structures
Column Buckling Laboratory: Worksheet
Student no.
Background theory
According to Trahair (2017) when a long-column straight beam that has a rectangular cross section is subjected
to a compressive axial load, so long as the beam remain straight, the beam can be analysed using compression
loads and tension loads. However, when the deflection becomes significantly large, a catastrophic failure is
experienced (Carrera, Pagani, and Banerjee, 2016). In such cases buckling theory is applied in the analysis of
the system. According to Euler buckling load theory, a buckling load, critical stress and the slenderness can be
computed from the following formulae shown below (Arani and Kolahchi, 2016)
The critical stress is evaluated from the formula
Slenderness ratio is computed from the formula
Where E is the modulus of elasticity of the material
I is the moment of the initial beam obtained from the formula I=bh3/12, b being the width of the beam and h
being the thickness of the beam
L is the length of the beam, A is the cross sectional area of the beam obtained from the formula A=bh and r is
the gyration radius about the bending axis
Aim of the experiment
This experiment is aimed at investigating the strength and failure angle of a typical aircraft stringer sections of
varied lengths. This will involve examining the failure and performance of the column and then comparing the
experimental findings with the theoretical predictions.
Theoretical Predictions (25%)
Second moment of area for flexural buckling calculations:
For a rectangle,
Coordinates of the Centroid
Yc = Σ (Ay)/ Σ (A)
Yc = y coordinate of centroid
Σ (Ay) = Sum of (each are times its centroid y coord)
Σ (A) = Sum of Areas
Xc = Σ (Ax)/ Σ (A)
Xc = x coordinate of centroid
Σ (Ax) = Sum of (each are times its centroid x coord)
Σ (A) = Sum of Areas
Since the structures are made of a combination of different rectangles, we use parallel axis theorem that leads to
I = Ic + Ad2
I = The second moment of area of that element about the combined centroid Neutral plane (x-x)
Ic = The second moment of area of that element about its own centroid
A = Area of that element
d = Distance from combined Neutral plane (x-x) to the centroid of that element
The results of calculations are shown in the appendices yielding
Ix= 1824.68

Iy= 1226.136
Ixy= 357.1161
Ix= 1683.977
Iy= 1181.239
Ixy= 180.8776
Ix= 1528.956
Iy= 1104.298
Ixy= 47.07887
Column 1, L=15
Column 1 L=15
Shortness or medium
Le=L for a column with both ends pinned.
L=382mm
W=21.49
Since
The column is long
flexural buckling load
since the column is long Pcr=Pe
Euler buckling for a pinned end column is
Local Buckling
Now k=4
So we have

Bottom lip
kN
Column 2, L=8
Column 2
Since L/W < 12 this is a short column
Flexural buckling load
Since the column is short, we use Rankine-Gordon formulae (Zhang &Liew, 2016)
Cross-sectional area = 51.244 mm2
Crushing load,
Buckling load,
Critical point loading = 32.54 kN
Column 3
Since L/W < 12 this is a short column
We use Rankine-Gordon formulae