Lect10 Columns Interaction Diagrams（Lect10列交互图）.pdf

`çäìãåë=fåíÉê~Åíáçå= aá~Öê~ãë rkfsbopfqv=lc=tfp`lkpfk=pqlrq `liibdb=lc=p`fbk`bI=qb`eklildvI=bkdfkbbofkdI=^ka=j^qebj^qf`p ib`qrob=u aêK=g~ëçå=bK=`Ü~ê~ä~ãÄáÇÉë `çäìãåë=Ó= `çãé~êÉ=j~íÉêá~äë Let’s try to visualize the effect of strength and the geometry that would correspond to a design for a specific load. Let’s take two very prominent materials: Steel: Esi Concrete: E=3600000psi It is obvious that in order to compensate the strength difference, we will address the geometric form, i.e. the cross sectional area. So a Steel column can be way more slender than a concrete column, just to bear the load. tÜ~í=fë=qÜÉ=bÑÑÉÅí=lÑ= `çäìãå=päÉåÇÉêåÉëë\ Imagine the effect of purely axial load applied in this element. What do you think will happen? Even if there is no shear or moment applied, do you believe that it will crush from the axial load? The uniformity and homogeneity of the material should be challenged. Even with prefabricated materials that are made under the strictest of regulations, we can expect some slight abnormalities. Those will render the element asymmetrical and stronger on one direction versus another. The formula that determines a column to be slender or not is the following: lu M 1 k≤⋅ −34 12 r M 2   `çäìãåë=Ó= päÉåÇÉêåÉëë This is a general method that we can roughly apply in order to consider how the connections can effect the strength of the column. More on this will be addressed during the next lectur