Geometry Of Sections: 1a. Stress Intro & Axial

In this video, I'd like to talk about stresses on structural members. It'll be mostly pictorial. We're going to look at some pictures. There might be a few arrows that you don't like. I know you don't like them, but there won't be any numbers, so don't panic. Okay, stresses. First of all, there is an externally applied force on a structural member. So there is a force, it causes a stress, but the stress is inside the member internally. And then as a result of stress, a strain shows up. So a strain is also external, and it's a manifestation of stress. So if you pull on a member, internally there is a tensile stress. The result, or the strain, is elongation. If you push down on a member, then you're compressing it, and there is a compressive stress, which shows up as a strain called shortening. It gets smaller. Likewise, if you apply a bending moment, then there is a bending stress, and the outcome of that, or the strain, is deflection. Very good. So, it is extremely important to distinguish the relationship between the axis of the structural member and the load. So if we have a load coming along the axis of the member, then we have something called an axial stress. That is that the force or the load is in line with the axis of the member. Whether the member is vertical or horizontal or inclined, as long as that force is in line with the axis of the member, it's called an axial force. and it results in axial stresses, pure axial tension and pure axial compression, depending if you're pulling or pushing. Excellent. However, if you apply a load perpendicular to the axis, then you are developing different type of stresses. Those are called perpendicular stresses or normal stresses, and they are basically a shear stress and a bending stress. So we're at the relationship of the load to the axis of the member. Here is a normal or a perpendicular load on a vertical member. Here is an axial load on an inclined member, but if you put it at a certain angle, then it might have two components and partially it's axial, partially it's perpendicular. So essentially, it is critical to determine the relationship between the line of action of the load and the axis of the member. Very good. So under axial stresses, we have compression and tension, and the force is along the axis of the member. Here's the member, Here's its axis. If you are pushing, then you have a compressive stress. If you are pulling along the axis, you have a tensile stress. And there is no shear, there is no bending if the load is purely in line with the axis of the member. Even if the member is horizontal and you're applying a load along the axis, then that's it. That's an axial load. In an arch, when you load an arch like this, it changes direction and goes along the axis of the member, of the arch. In a shallow arch, there is something called thrust, which is basically the arch wants to spread. So it wants to do that. So we need to contain it. There needs to be a reaction to the thrust. The horizontal component is called thrust. And the shallower the arch, the greater the thrust. There is still a vertical reaction, but if the arch is shallow, then the thrust is much greater than the vertical. So T is greater than the vertical reaction. However, if the arch is steep, then the vertical reaction is much more than the horizontal thrust and the reaction needed to contain it. The same is true for a cable. The cable is a mirror image of an arch. So, whereas the arch is in compression, when you pull on a cable, it changes its shape because it's flexible but the load is resisted along the axis of the cable and definitely in tension. Very good. So types of stresses axial stresses are compressive stresses and tensile stresses versus perpendicular stresses. Perpendicular stresses occur when you have a span. If a member is spanning and the load is perpendicular to the axis, such as a concentrated load or uniform load, the relationship to the axis is a perpendicular relationship. Therefore, what results in this case is sheer force and bending moment force, and the stresses that result from a sheer force is a sheer stress, And from a bending moment force, there is a stress called a bending stress. And each material has a certain ability in compressive stress, tensile stress, shear stress, bending stress. If that capacity is exceeded, the member fails either in tension or in compression or in shear or in bending. Very good. So if you load the beam this way, then you're loading it along the axis. That's a different story, extension or compression. If the member is vertical, such as a mullion in a curtain wall or a sheet of glass, and you load it with wind load, that is still a relationship which is perpendicular to the axis. And it will result in shear and bending. The member will tend to do that. If the member is inclined, it doesn't matter where is its axis, over here. If you load it this way, then that one has two components. We're going to resolve it into two components. And this is an axial component. And the other one is a perpendicular component. The axial component will create either tension or compression, in this case compression. Nice word here. Perpendicular. Okay. And the perpendicular component of the force will cause shear and bending. Excellent. So please, important to determine the orientation of the load with respect to the axis of the member. It's either axial, tension, and compression, or else it's perpendicular, shear, and bending. Very good. So under axial, we have columns are typically loaded along their axis, usually in compression. Piles are the same. A load comes down here and is transferred from the pile cap into the members along their axis, into the piles along their axis. Foundation is another example of an axial load where a column is taking a compression load and then it transfers it to a larger foundation and then off to the soil. Trusses, truss members are always assumed to be in pure tension compression, ideally, theoretically. In the real world, that's not true. But for analysis purposes, trusses, each member of the truss is loaded axially. Although the truss is a spanning member between these two points, it does shear and bending as a collective. But individually, every member of the truss is doing either tension or compression. In this image, red is compression, blue is tension. So in a truss like this that is loaded with gravity loads, the top cord is usually in compression. The bottom cord is usually in tension. So regardless of the orientation of the web members, The top is in redness and the bottom is in blueness. Very good. We'll talk about trusses in a different video. Diagonal bracing is another example of an axially loaded member because when you have a member pushing on a truss such as this one, the load comes down that diagonal member and ends up in the ground like this. Or if you were pulling on a member, in this case, if the load is coming from this direction, it's as if it is pulling on the cable. And so the cable is responsible for that load. It is that you don't load diagonal bracing this way. That's not the way it's meant to take the load. Diagonal bracing is there to take lateral load from wind or earthquake. Diagonal bracing is not a gravity member. The beams and the columns are gravity members. They take live load, dead load. The diagonals are there for lateral loads. Excellent. Arches and cables, also examples of axial loading. Versus perpendicular loads. There has to be a span. That is very critical. If a member is spanning, that's it. It's subjected to shear and bending stresses. So roofs, floors, slabs, decks, all these guys span. If they span, they bend, and they're subjected to shear. Purlins, joists, open-web joists, wood joists, concrete joists, all of them span. and they're subjected to shear and bending beams and girders clearly a shear wall is a lateral resisting member that takes loads in plane and it's subjected to shear it gets a lateral load from wind for example or earthquake and it resists it at its foundation when you have forces that are in opposite directions you get shear most important is this note here this is where shear is critical it's at connections shear failure happens at the connection whether it's a simpson joist hanger or whatever connector you have in wood or bolts whether it's a steel connection and you have bolted connection or you have a welded connection, all of these are subjected to shear. In reinforced concrete, the stirrup is in charge of shear. Okay, a moment frame in contrast to a braced frame, a moment frame is mostly doing bending and resisting load by bending versus a diagonal brace is resisting lateral load by compression or tension. Very good. A lintel is another example of a spanning member that is subjected to load. We'll see lintels a little bit further on in this video. Excellent. So let's discuss further axial loads. So if we look at these two brackets that are hanging from this wall, first of all, you should notice that they're not in the same orientation. So here I am pushing down on one of these, the one on the left. As the force comes down here, let's use a color that is seen. As the force comes down here, maybe a little more line weight. as the force comes down here, this member has to go into compression. It's like saying the member is pushing on the bracket. And the one on the top is going to stretch. This is a triangle. It's a truss. The top one is being pulled out of the wall. The bottom one, the diagonal is being pushed into the wall. Excellent. So looking here at this image on the left, if there is a snow load or if there is any kind of rain load on that top of this roof, it is going to push down and these two members have to respond to that load and they end up pushing into their supports. So that's an example of axial along the direction of that diagonal axial compression. However, if the wind comes in here and pulls up, if the wind comes in from underneath and pushes the roof upward, then this will go into tension and try to hold down the roof from flying out. So then it ends up pulling. And we have an example of axial tension if there is wind uplift on that roof. Same here, we have this funky looking canopy, but there is a weight and there is a load here and this load is going to a spanning member. This member spans. It's supported here and here. And if the member spans, then it is going to be in shear and bending. But then the support itself is taking the load along its axis, and the load is pushing down. And so this member is in compression, this member is in compression, this member is in compression sorry axial compression very good um let's understand a little bit more here we go this is the OCAD the Ontario College of Art Design and Design in Toronto we have this big box sitting on stilts and these stilts are clearly in compression because they have to carry that weight and it's axial because it's along the length of the members critical whenever you have compression another word that comes up immediately with compression is slenderness how slender is the member is it going to fit if it's short and fat it'll fail in crushing if it's tall and skinny it's slender and therefore we're worried more about buckling So these are pretty slender columns, so they have to be checked for buckling. Looking at this bridge, I'd like to say that whenever you see skinny in steel, that has to be tensioned. Whenever you see chunky in steel, it has to be compressioned. So, clearly, these members are in tension. These members are in tension and they're in pairs. And the top is in compression. So are these members. You can see it. It's chunky. Whenever it's chunky in steel, it's got to be compression. Very good. So finally, looking at this image here, we have the top level column. Then it's increasing in size as it picks up load. The column gets larger and larger. All of these are axially loaded columns. They might have a little bit of eccentricity. We'll get to that later. But assume for now it's axial along the axis of the member. Excellent. So let's look at tension, axial tension. Now this bracket we said when the load comes down here, this guy has to fight. So it's in compression and it's pushing into the wall. Now this other one, on the other hand, I'm pulling down on it. And this member has to stretch. it has to keep the bracket attached to the wall, so it's in axial tension. The bottom one is being pushed, and so it's in compression. As a general rule, there are always exceptions to the rule, but if you are considering a member below a member, if you are considering something that is below a structure, then it's usually compression. If it's above, then it's usually tension. Okay, let's see if we can make sense out of this. Here are cables cannot do compression. They're always in tension. So if you see a cable that is chilled out like this, it means it's in compression. It still hasn't been tightened, or else it was pushed beyond its limit in compression, and it's slacking. A cable should be taut, okay? Something like that, okay. That's a cable that is in tension, or a tie rod. Very good. Let's look at this very, very ugly canopy. the member, sorry, the tie rods are above the canopy. So they must be in tension. They're hanging. They're hanging the canopy and tying it back to the wall. Now, I like this picture. It's very ugly, but I like it because it helps me explain that the shallower the angle of these tie rods, the shallower the angle, the more horizontal the member. The more horizontal the member, it's not very effective in carrying vertical gravity loads. The steeper the member, this member is steeper than the short one. So the steeper the member, then the more vertical the member, then the more effective it is in carrying vertical gravity load, the less effective it is in carrying lateral loads. So in summary, a vertical member cannot do lateral load. Likewise, a horizontal member cannot carry vertical loads. So the steeper this angle, the more effective it is in carrying gravity. If you could tie it from the sky, it's 100% efficient, but the shallower it gets, the less effective. So these guys here, the shorter ones, are doing less work than the ones that are steeper. Excellent. So here's another example. Based on that angle, if it were up to here, then it would have been a smaller cable. The shallower it is, the beefier it needs to be because it's carrying a bigger horizontal component. Excellent. Both canopies are ugly. Let's look at one that's a little bit nicer, more designy, a pair of angles. And they're attached here and going back. And that angle is pretty steep. And therefore, the cable, we can get away with something pretty small. Excellent. So here, clearly, in a truss, always spanning between here and somewhere here. The top is in compression and the bottom is in tension. And we have a bunch of cables must be they're all in tension. We looked at this example and we saw that the thin guys are always in tension. Sorry, in steel, it's very easy to tell the difference. If this were wood, the members I couldn't distinguish between their size because wood is reasonably capable in compression and intention, but steel is superior intention. And it freaks out in compression because of buckling and slenderness. Very good. Let's look at this truss. The top of the truss, the top cord of the truss is in compression. So in this case, it's a glue lamp member. Okay. Glue lamp is chunky and it can handle compression very nicely. But if you look at the bottom cord, it's very slender, very thin, because it's in tension. Likewise, if we look at the diagonals, this member here is in tension, because it's pretty skinny, versus this member here is in compression, and it's beefier. It has more material so that it doesn't buckle under compression. If we look at the exterior of this space, the glulam member continues to the outside. And then there's a compression member here. Because if there's a wind load hitting the roof on the top, then this guy goes into compression. If the wind comes from underneath and pulls up that roof, this guy goes into tension. So it's got to be able to do compression and tension because wind could come from above the roof or uplift the roof itself. So you cannot put a cable there because it'll fail when there is a large load on top of the roof, snow or otherwise. Very good. So here's another example. This is a beautiful church outside of Dallas in Richmond. It's the Cistercian Chapel. And the top, these rafters are made of wood. They're in compression. And then if you notice, to triangulate those two red members, there's a very thin cable here that keeps those two rafters from spreading. So it goes into tension. And if we look closely at the detail, you can see here the cable going through. And here's the rafter coming down. It pushes. The rafter pushes on this member. This member pushes back. And the cable is also keeping it from going. So the cable intention is also going in that direction. and preventing it from spreading. And the vertical component, oops, let's use the right color, the vertical component of that diagonal force is taken up by this piece of steel and sends it into the stone. So I have a diagonal member coming here. It has two components, one, two. And I will fight you back and there is a cable here. The cable is in tension so the two of us are going to fight that horizontal component but I am also capable vertically in order to resist the vertical component. Excellent. So here's the Texans training facility in Houston. It's a pneumatic structure. is filled with air. So it's very light and it wants to go up because it's filled with air. So you look at the foundation and you see it's very simply a cable that keeps this thing from flying away. So the foundation on this one is very small because the weight is taken up by the cables and they pull up just a little bit on the foundation. It's not a deep foundation because there's not that much compression. Okay, so let me stop the recording here and then we'll start over with perpendicular stresses in the same type of presentation.