1. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman Eureka Museum, Ballarat 1/16 l Tension members occur in trusses, and in some special structures l Load is usually self-aligning l Efficient use of material Stress = Force / Area l The connections are the hardest part

2. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l For short piers, Stress = Force / Area Slender columns, Uni swimming pool Squat brick piers 2/16 l Load is seldom exactly axial l For long columns, buckling becomes a problem

3. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l Member will only fail in true compression (by squashing) - if fairly short short column l Otherwise will buckle before full compressive strength reached long column 3/16

4. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l Horizontal load x height W P e R = W + P M OTM = Pe 4/16 y H R = W M OTM = Hy W R = H l Load x eccentricty

5. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l The average compressive stress = Force / Area l But it isn’t uniform across the section l Stresses can be superimposed PP e = compressive stress = tensile stress M Stress diagrams P only M only 5/16 P and M added

6. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l Stress due to vertical load is P / A, all compression l Stress due to OTM is M / Z, tension one side and compression on the other l Is the tension part big enough to overcome the compression? l What happens if it is? 6/16

7. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l If eccentricity is small, P/A is bigger than Pe/Z P and M added 7/16 P onlySmaller M only P and M added P/A Pe/Z P onlyLarger M only Tension P/A Pe/Z l If eccentricity is larger, Pe/Z increases l Concrete doesn’t stick to dirt — tension can’t develop!

8. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l For a rectangular pier — l Reaction within middle third, no tension l Reaction outside middle third, tension tries to develop 8/16 Within middle thirdLimitOutside middle third

9. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l The overturning effect is similar to eccentric loading l We treat them similarly l There is only the weight of the pier itself to provide compression y H W R = W M OTM = Hy 9/16 R = H

10. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman Extra load helps to increase the compression effect, and counteract tension Pinnacles add load 10/16 Stress diagrams = compression = tension P H y Some tension occurs H 2P Extra load avoids tension

11. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l Will it sink? (Can the material stand the maximum compressive stress?) 11/16 l Will it overturn? l Reaction within the middle third — factor of safety against overturning > 3 l Reaction outside middle third — factor of safety inadequate 1 - 3 l Reaction outside base — no factor of safety

12. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l A slender column buckles before it squashes l A slender column looks slender l We can quantify slenderness by a ratio — l The slenderness ratio is L/B or L/ r, where l The minimum breadth, B, or the radius of gyration, - r l The effective length, L 12/16

13. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l For timber and concrete — limit for L/B is about 20 to 30 l For steel, limit of L/ r is about 180 l At these limits, the capacity is very low: for efficient use of material, the ratios should be lower l Note - effective length (depends on end-conditions) 13/16

14. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l The buckling stress increases with E ç(so steel is better than aluminium) l The buckling stress reduces with (L/ r ) 2 ç(so a section with a bigger r is better) 14/16

15. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l L/ r may be different in each direction çthe smaller r is the critical one l Can we support the column to reduce L? l Can we use a section with a bigger r in both directions? 15/16

16. University of Sydney –Building Principles Axial Forces Peter Smith& Mike Rosenman l Tubular sections are stiff all ways l Wide-flange H-beams better than I-beams l Squarish timber posts rather than rectangular = better sections for columns 16/16