Lab #8 will involve the development of deflection curves for columns undergoing loading and with differing end conditions.

When a column is loaded in axial compression, the system will remain stable as long as the applied load is smaller than the Euler buckling or critical load, P_{cr}. A stable system is a system which returns to equilibrium when the load is removed.

As the applied load exceeds P_{cr}, the system becomes unstable, resulting in column bending and ultimate failure. The value of P_{cr} varies with the end conditions for the column. The following relationships have been established for common end conditions:

n = 1, 2, 3, ...

The value of n is determined by the boundary conditions. For a column with both ends pinned, n = 1. For a pinned-clamped column, n = 1.414. For a clamped-clamped column n = 2.

Description of Experiment

Column Deflection and Critical Loads

Equipment needed

Strut machine

Aluminum, brass, and steel specimens

Yard stick or tape measure

Calculator

Procedure

Prior to starting the lab exercise, measure the aluminum, brass, and steel specimens.

Assuming that E = 73 GPa for aluminum, 100 GPa for brass, and 200 GPa for steel, calculate the value of the critical load, P_{cr}, for pinned-pinned, pinned-clamped, and clamped-clamped end conditions.

Determine three loads which will be applied to the column, 25%, 50% and 75% of P_{cr}.

Place the column in the strut machine.

Mark the specimen in two-inch increments.

Apply the first load, and use the dial indicator to obtain the deflection every two inches down the length of the column.

Repeat for the remaining loads, end conditions, and specimens.

Elements to include in your report

Your lab report must include at least the following:

Calculations for determining the critical load for each specimen.

Plot the deflection curves for each type of material and end condition. Plot all three loads for each respective end condition on the same graph.