EMA 3702L: MECHANICS AND MATERIALS SCIENCE LAB

Euler Buckling

Objectives

To understand the buckling failure of materials. To determine the critical (or Euler) buckling load or critical stress, and slenderness ratio by performing a buckling experiment on the various length beams with a rectangular cross section. To compare the experimental results with the theoretical calculations.

Introduction

A long-column straight beam with a rectangular cross section is subjected to a compressive axial load. As long as the beam remains straight, it can be analyzed by the theories of tension or compression loads; however, if the deflection become suddenly large and leads to catastrophic failure, the buckling theory has to be applied for the analysis. According to the theory, the critical (or Euler) buckling load P_cr, critical stress s_cr, and slenderness ratio L/r can be calculated by the following formulas:

where: E is the modulus of elasticity.

I is the moment of initial of the beam, I = b h³ / 12. b is the width of the beam and h is the thickness of the beam.

L is the length of the beam.

A is the cross section area of the beam, A = bh.

r is the radius of gyration about the axis of bending.

In the experiment, the critical (or Euler) buckling load P_cr,exp can be determined by using a calibration formula: maximum deflection Dx_max, which is recorded from a dial test indicator, multiplies by 2800 blf / in.

and critical stress s_cr,exp can be obtain as:

Procedures

Step 1. Measure the cross section size of the testing beam (width b and thickness h), and note its material.

Step 2. Mount the beam in the apparatus and turn the screw jack until the beam is held in place in the grips and the dial indicator (in the force ring) just begins to show deflection.

Step 3. Measure the length L of the beam between the two grips.

Step 4. Slowly turn the screw jack and watch the beam for buckling.

Step 5. When buckling begins to occur, the deflection in the dial indicator will reach a maximum value and no longer increase as the beam buckles under the load. Record the deflection Dx_max.

Step 6. Use other different length beams, repeat the entire process.

Analysis and Discussion

For each of the tested beams, determine the theoretical and experimental critical buckling load and stress. Input data should include beam dimensions and material properties and the deflection of the dial indicator when buckling occurs, and calculate the slenderness ratio for each beam. Show the results in an organized table and a plot of buckling stress vs. slenderness ratio. Find a best fitting line or curve for the experimental data. Compare the experimental results to the analytical calculations.

Report Requirement

A technical version report must be submitted both printed and electronic copies on the due date (see the announcement board).