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

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

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

University of Sydney –Building Principles AXIAL FORCES Peter Smith& Mike Rosenman l Horizontal load x height l Load x eccentricity y H W P e R = W R = W + P MM OTM = HyOTM = Pe W

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 Elevation P Plan Stress diagrams P e b d = compressive stress = tensile stress M P onlyM onlyP and M added

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?

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

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 Within middle thirdLimitOutside middle third

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 = WM OTM = Hy

University of Sydney –Building Principles AXIAL FORCES Peter Smith& Mike Rosenman Extra load helps to increase the compression effect, and counteract tension 2P Elevation P Plan HH y = compression = tension Stress diagrams Some tension occurs Extra load avoids tension Pinnacles add load

University of Sydney –Building Principles AXIAL FORCES Peter Smith& Mike Rosenman l Will it sink? (Can the material stand the maximum compressive stress?) l Will it overturn? l Reaction within the middle third — factor of safety against overturning usually between 2 and 3 l Reaction outside middle third — factor of safety inadequate l Reaction outside base — no factor of safety

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 minimum breadth, B, or the radius of gyration, - r l The effective length, L l The slenderness ratio is L/B or L/ r

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)

University of Sydney –Building Principles AXIAL FORCES Peter Smith& Mike Rosenman l The buckling stress increases with E  (so steel is better than aluminium) l The buckling stress reduces with (L/ r ) 2  (so a section with a bigger r is better)

University of Sydney –Building Principles AXIAL FORCES Peter Smith& Mike Rosenman l L/ r may be different in each direction  the 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?

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