Axial tension members轴拉构件

1、University of Sydney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lTension members occur in trusses, and in some special structures lLoad is usually self- aligning lEfficient use of material lStress = Force / Area lThe connections are the hardest part M a c in to s h P IC T im a g e fo

2、 rm a t is n o t s u p p o rte d Eureka Museum, Ballarat University of Sydney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lFor short piers, Stress = Force / Area lFor long columns, buckling becomes a problem lLoad is seldom exactly axialM a c in to s h P IC T im a g e fo rm a t is n o

3、 t s u p p o rte d Slender columns, Uni swimming pool Macintosh PICT image format is not supported Squat brick piers University of Sydney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lMember will only fail in true compression (by squashing) - if fairly short short column lOtherwise wil

4、l buckle before full compressive strength reached long column University of Sydney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lHorizontal load x height lLoad x eccentricity y H W P e R = W R = W + P MM OTM = HyOTM = Pe W University of Sydney Building PrinciplesAXIAL FORCES Peter Smit

5、h& Mike Rosenman lThe average compressive stress = Force / Area lBut it isnt uniform across the section lStresses 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 PrinciplesAXIAL FORCES Peter

6、Smith& Mike Rosenman lStress due to vertical load is P / A, all compression lStress due to OTM is M / Z, tension one side and compression on the other lIs the tension part big enough to overcome the compression? lWhat happens if it is? University of Sydney Building PrinciplesAXIAL FORCES Peter Smith

7、& Mike Rosenman lIf eccentricity is small, P/A is bigger than Pe/Z lIf eccentricity is larger, Pe/Z increases lConcrete doesnt stick to dirt tension cant develop! P onlyLarger M only P and M added P onlySmaller M only P and M added Tension University of Sydney Building PrinciplesAXIAL FORCES Peter S

8、mith& Mike Rosenman lFor a rectangular pier lReaction within middle third, no tension lReaction outside middle third, tension tries to develop Within middle thirdLimitOutside middle third University of Sydney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lThe overturning effect is simil

9、ar to eccentric loading lWe treat them similarly lThere is only the weight of the pier itself to provide compression y H W R = WM OTM = Hy University of Sydney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lExtra load helps to increase the compression effect, and counteract tension 2P E

10、levation P Plan HH y = compression = tension Stress diagrams Some tension occurs Extra load avoids tension Macintosh PICT image format is not supported Pinnacles add load University of Sydney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lWill it sink? (Can the material stand the maximu

11、m compressive stress?) lWill it overturn? lReaction within the middle third factor of safety against overturning usually between 2 and 3 lReaction outside middle third factor of safety inadequate lReaction outside base no factor of safety University of Sydney Building PrinciplesAXIAL FORCES Peter Sm

12、ith& Mike Rosenman lA slender column buckles before it squashes lA slender column looks slender lWe can quantify slenderness by a ratio lThe minimum breadth, B, or the radius of gyration, - r lThe effective length, L lThe slenderness ratio is L/B or L/r University of Sydney Building PrinciplesAXIAL

13、FORCES Peter Smith& Mike Rosenman lFor timber and concrete limit for L/B is about 20 to 30 lFor steel, limit of L/r is about 180 lAt these limits, the capacity is very low: for efficient use of material, the ratios should be lower lNote - effective length (depends on end-conditions) University of Sy

14、dney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lThe buckling stress increases with E (so steel is better than aluminium) lThe buckling stress reduces with (L/r)2 (so a section with a bigger r is better) University of Sydney Building PrinciplesAXIAL FORCES Peter Smith& Mike Rosenman lL/r may be different in each direction the smaller r is the critical one lCan we support the column to reduce L? lCan we use a section with a bigger r in both directions? Univer