Tension members occur in trusses, and in some special structures Load is usually self-aligning

1. Axial Tension Members Eureka Museum, Ballarat • Tension members occur in trusses, and in some special structures • Load is usually self-aligning • Efficient use of material • Stress = Force / Area • The connections are the hardest part

2. Axially Loaded Piers • For short piers, Stress = Force / Area • For long columns, buckling becomes a problem • Load is seldom exactly axial Slender columns, Uni swimming pool Squat brick piers

3. Axially Loaded Piers (cont.) • Member will only fail in true compression (by squashing) - if fairly short short column • Otherwise will buckle before full compressive strength reached long column

4. The Overturning Moment (OTM) • Horizontal load x height • Load x eccentricity e P W W OTM = Hy OTM = Pe H y R = W + P M M R = W

5. Eccentrically Loaded Piers P P M • The average compressive stress = Force / Area • But it isn’t uniform across the section • Stresses can be superimposed e d Elevation b Plan P only M only P and M added = compressive stress = tensile stress Stress diagrams

6. Does Tension Develop? • Stress due to vertical load is P / A, all compression • Stress due to OTM is M / Z, tension one side and compression on the other • Is the tension part big enough to overcome the compression? • What happens if it is?

7. Does Tension Develop? (cont.) • If eccentricity is small, P/A is bigger than Pe/Z • If eccentricity is larger, Pe/Z increases • Concrete doesn’t stick to dirt — tension can’t develop! P only Smaller M only P and M added Tension P only Larger M only P and M added

8. Middle-Third Rule the limiting case • For a rectangular pier — • Reaction within middle third, no tension • Reaction outside middle third, tension tries to develop Within middle third Limit Outside middle third

9. Horizontal Loads on Piers • The overturning effect is similar to eccentric loading • We treat them similarly • There is only the weight of the pier itself to provide compression W OTM = Hy H y M R = W

10. Extra Weight Helps • Extra load helps to increase the compression effect, and counteract tension 2P P H H Some tension occurs y Pinnacles add load Elevation Extra load avoids tension Plan Stress diagrams = compression = tension

11. How Safe is my Pier? • Will it sink? (Can the material stand the maximum compressive stress?) • Will it overturn? • Reaction within the middle third — factor of safety against overturning usually between 2 and 3 • Reaction outside middle third — factor of safety inadequate • Reaction outside base — no factor of safety

12. Slender Columns • A slender column buckles before it squashes • A slender column looks slender • We can quantify slenderness by a ratio — • The minimum breadth, B, or the radius of gyration, - r • The effective length, L • The slenderness ratio is L/B or L/r

13. The Slenderness Ratio • For timber and concrete — limit for L/B is about 20 to 30 • For steel, limit of L/r is about 180 • At these limits, the capacity is very low: for efficient use of material, the ratios should be lower • Note - effective length (depends on end-conditions)

14. The Buckling Stress • The buckling stress increases with E • (so steel is better than aluminium) • The buckling stress reduces with (L/r)2 • (so a section with a bigger r is better)

15. How do we Improve the Performance? • L/r may be different in each direction • the smaller r is the critical one • Can we support the column to reduce L? • Can we use a section with a bigger r in both directions?

16. Good Sections for Columns • Tubular sections are stiff all ways • Wide-flange (H) beams better than I-beams • Squarish timber posts rather than rectangular = better sections for columns