L5 Boundary Conditions

Añadido: 2026-05-31

[00:00:00]welcome to week three everyone hopefully that foam demonstration was helpful for you as we continue our discussion of structural analysis this week with perpendicular forces I do apologize if the video seemed a bit wobbly toward the end but I don't actually have a digital camera or a tripod so I had to get a little creative and I'll put up a picture here to show you what I'm talking about yep that right there is what we'll call uh engineering Ingenuity I guess anyway I'd like to take a step back for just a moment before we continue any further by talking about boundary conditions or end conditions as we called them in our buckling equation and this should be review from structures one but I wanted to give you a brief refresher of what these different symbols actually mean and provide you with some real world examples note that we are only discussing 2D structural analysis in this course we'll leave the 3D calculations to the structural engineers so let's start with a roller a roller provides only one reaction in One Direction it does not provide any restraint against lateral translation or rotation so if we looked at its response to loading here it would look like this there would be no change in the vertical position of the member at the location of the roller however the roller will allow the member to translate horizontally as well as rotate freely and so we only have one reaction in the vertical direction or we can also turn the roller on its side like this and in this case the roller only provides restraint against lateral translation next we have a pin similar to a roller a pin allows the member to rotate freely however in addition to providing a vertical reaction a pin now also offers restraint against lateral translation lastly we have our fixed condition and here we have restraint against all three types of movement we have restraint in the vertical Direction restraint in the horizontal Direction and restraint against rotation at the end of the member and so you can see in this response to loading diagram at the location of the fixity the member will remain at 90 degrees we can also talk about these unconditions in terms of joints between two members in the case of a pinned joint if we were to load this horizontal member it would be free to rotate about the joint however the vertical and the horizontal forces would translate through the joint and into the perpendicular member lastly we have a rigid joint like the pin joint we are passing our vertical and horizontal forces from one member to the other in addition we are also passing rotation from one member to the other and so the angle between the two members remains at 90 degrees now let's take a look at some real world examples of these different end conditions now let's take a look at some real world examples of these different boundary conditions and let's start with rollers so this hanger here would be considered a roller we are providing a vertical reaction to support the weight of this pipe however we are not providing any restraint in the X Direction along the member and so we would draw that like this with this blue line representing the pipe the reason we often use rollers for pipe supports is because pipes are often made of some type of metal and Metal of course as it heats up and cools down will expand and contract and so there will be some elongation along the x-axis Direction and as we learned in week one if we restrain that change in length we will create forces or stresses in the pipe so instead we want this pipe to be able to change length freely without restraint and roll over the top of this support our next roller condition is precast concrete and Precast of course means that these concrete pieces are cast or formed somewhere else off-site and brought onto the site as big pieces kind of like building blocks and often these pieces are wide enough and massive enough that we can simply rest one piece on top of the other without providing much restraint and the total structure will still remain stable so what is often in the case with parking garages we will lay this precast concrete Beam on top of this concrete Coral without any real rigid connection between the two pieces and so in this case we would also refer to this condition as a roller support now let's move on to pin connections and the first type of pin connection we're going to talk about is a steel pinned connection so when you look at a steel connection if you see that only the webs of the supported member are connected to the supporting member in this case this column then we know that this is a pin connection and you can see here in this photo that there is daylight between the flanges of the supported member and the column so only the web is connected to the supporting column therefore we will only be passing a vertical force from the beam into the column as well as any horizontal or axial forces that we may have in these beams but we will not be passing any moment from our supported beam to our supporting column with this type of connection similarly with a joist seat we will pass our vertical force from our joists into this supporting beam here as well as any horizontal or axial force in the top chord of this joist and so we will have a reaction here and a reaction like this note that the bottom cord is not connected to the supporting beam also note that most wood connections are pinned connections it is very difficult to achieve a fixed connection with wood also if we take a look at our Precast again however this time we have two steel plates connected to these Precast members and we are applying a weld between the two now we can call this a pinned connection where we can pass a vertical Force into the supporting column as well as an axial Force lastly let's look at a base plate example and a base plate is what we will have between a column and a peer which is a foundation element which we will discuss later in this course so if we have a base plate that has bolts only located between the flanges of the column then this will be a pinned support we will be able to pass our vertical reaction into the foundation as well as any horizontal Force however we won't be able to pass any moment that there happens to be at the base of this column now let's move on to fixed connections and we'll start with a steel connection from a beam to a column as we saw earlier but now note that we are welding the top flange and the bottom flange to our supporting member and note that this supporting member could be a column or a beam in this condition now that we have provided a connection between the flanges to the supporting member now we can pass a moment from our supported beam into our supporting column so a fixed connection requires that we attach either by welding or bolting both the top and bottom flange of Our member to our supporting member our next fixed condition is cast in place concrete cast in place concrete is of course cast monolithically meaning that this entire member is cast as one piece both column and beam and so of course any bending that occurs in the beam will pass into the column finally let's look at some real examples of pinned and fixed joints pinned joints are what you will often find in typical steel and wood framing so the connection between a steel or wood beam to a steel or wood column will typically be pinned also the joints between truss elements and Arch elements will also be pinned finally the joints between all the elements of a steel braced frame including the brace itself all of those joints will also be pinned there will be no restraint against rotation at any of these joints with fixed joints of course the obvious example is a moment frame moment frames and Brace frames we will be talking about more in depth later in the course trusses and arches we will be discussing next week for this week we will be focusing only on beams and our next topic will be how to solve for reactions at either end of a beam