Objectives, Lab #8

Column Deflection and Critical Loads

Back to main page
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.

Back to main page