Solid Mechanics
02TTB204 Mechanics of Solids
Part B Lab Buckling of Struts
1. Introduction
The task was given to obtain the buckling stresses for pin-ended steel struts of various slenderness ratios and compare with theoretical predictions obtained using the Euler and Rankine-Gordon equations.
2. Theory
The method of obtaining the buckling stresses followed was to use data show in Appendix A. From the record of applied load, P, against deflection, δ, a Southwell plot of δ against δ/P can be drawn. The gradient of the Southwell plot yields the buckling load of the particular strut. The dimensions of each strut are given and therefore the experimental critical stresses can be obtained by division of the buckling load by the cross-sectional area. When taking data from the plot in Appendix A, it is only necessary to take values around the region where buckling occurs (These are highlighted red on the plot).
Ideally the experimental buckling stresses obtained should be closely linked to two theoretical methods for obtaining the same stresses. Eq.2.1 and Eq.2.2 both give methods of calculating the buckling stress in a strut.
Euler equation: - Eq.2.1
Rankine Gordon:- Eq.2.2
Fig.2.1 shows a perfect pin-ended strut. This strut is assumed to undergo only axial loading and will remain in its elastic range prior to the critical load being reached. Deflection will only occur when the critical load is reached. Any deflections prior to this load are maintained inside the structure.
Fig.2.1 a) Perfect pin-ended strut b) Deflection due to buckling
3. Discussion
3.1 Differences between two theories
Euler theory states that provided the critical buckling load is not exceeded a strut will not undergo any excessive deflection and will remain in equilibrium, i.e. the strut will only buckle if the applied load exceeds the critical load, it will not yield or fail in any other way before this point.
Experimentally real struts do
Part B Lab Buckling of Struts
1. Introduction
The task was given to obtain the buckling stresses for pin-ended steel struts of various slenderness ratios and compare with theoretical predictions obtained using the Euler and Rankine-Gordon equations.
2. Theory
The method of obtaining the buckling stresses followed was to use data show in Appendix A. From the record of applied load, P, against deflection, δ, a Southwell plot of δ against δ/P can be drawn. The gradient of the Southwell plot yields the buckling load of the particular strut. The dimensions of each strut are given and therefore the experimental critical stresses can be obtained by division of the buckling load by the cross-sectional area. When taking data from the plot in Appendix A, it is only necessary to take values around the region where buckling occurs (These are highlighted red on the plot).
Ideally the experimental buckling stresses obtained should be closely linked to two theoretical methods for obtaining the same stresses. Eq.2.1 and Eq.2.2 both give methods of calculating the buckling stress in a strut.
Euler equation: - Eq.2.1
Rankine Gordon:- Eq.2.2
Fig.2.1 shows a perfect pin-ended strut. This strut is assumed to undergo only axial loading and will remain in its elastic range prior to the critical load being reached. Deflection will only occur when the critical load is reached. Any deflections prior to this load are maintained inside the structure.
Fig.2.1 a) Perfect pin-ended strut b) Deflection due to buckling
3. Discussion
3.1 Differences between two theories
Euler theory states that provided the critical buckling load is not exceeded a strut will not undergo any excessive deflection and will remain in equilibrium, i.e. the strut will only buckle if the applied load exceeds the critical load, it will not yield or fail in any other way before this point.
Experimentally real struts do
References: Longman, 1996 ISBN:- 0-582-25164-8 Blackwell Scientific Publications, 1989 ISBN:- 0-632-02018-0