L8 Lateral System

Added: 2026-05-30

[00:00:00]hello and welcome to week five more than halfway through now hopefully you are all ready to wrap up this chapter in our semester on structural analysis now that we've covered truss analysis the rest of the math for this semester should be significantly easier so way back in week one we broke apart the typical loads on a building into gravity loads and lateral loads and we did this because of building superstructure is typically broken down similarly we have our gravity system to support the gravity loads then we have our lateral system to support lateral loads up until now we have talked primarily about the gravity system and we have learned about the behavior of several gravity system elements such as the floor slab beams girders trusses arches cables and columns this week we will be diving deeper into the lateral system but our discussion of lateral Force resisting elements will not be nearly as in-depth as our gravity discussion in previous weeks due to time constraints also as I've said before lateral is significantly more complex than gravity so let's save the really complex stuff for the structural engineers anyway as with the gravity system lateral loads also start in the slab and when we talk about the lateral system we often refer to the slab as the building's diaphragm the diaphragm distributes the lateral load to the lateral resisting Elements which can be moment frames brace frames or Shear walls and keep in mind that just because a structural element is used in the building's lateral system does not necessarily exclude it from the building's gravity system in fact many structural lateral elements will also serve a dual purpose in the gravity system for example as we just mentioned the slab is both a gravity and a lateral element similarly moment frame and Brace frame beams and columns and lastly Shear walls will also take both gravity and lateral forces if we look back to the example steel building that we saw in week one we can see here that there are several beams and columns in this building that participate in both the gravity and lateral systems now let's first talk more generally about the best way to lay out lateral resisting elements before we dive deeper into each specific type lateral Force resisting systems should be as close to symmetrical as possible to reduce torsion and increase efficiency we already mentioned this previously in our week two discussion of seismic forces hopefully it made sense to you then but just in case it didn't we're going to review now in Greater detail so looking at these two layouts it may not look to you like either of these layouts is particularly symmetrical but let's consider that each element acts primarily in Only One Direction that is these first three elements in this layout will primarily resist forces in this direction the other two elements will primarily resist forces in this direction along their length so really it's only the perpendicular distance that matters so if I take this element here and slide it parallel to its length like that it doesn't really change the behavior of the overall system so ultimately we can simplify these layouts to beam analogies hopefully then the symmetry of one of these two layouts becomes more clear so first let's focus on the Y Direction and the elements resisting the force in the y direction will again be these two on either side for this layout so if we simplify the layout of these elements to a beam analogy we can see we have two supports provided at either end to resist this lateral force in the y direction thus the force in each element will be roughly equal with the other layout however we have two supports very close to each other and pushed to one side this complicates the load path and we end up with significantly higher forces in these supports compared to the previous layout similarly in the X Direction we see in the top layout that the lateral elements resisting forces in the X Direction are laid out roughly symmetrically however in the second layout they are again pushed down to one side so now hopefully you can see that the left layout is more efficient than the right or lateral loads in both the X and the Y directions so with that being said let's jump into our first lateral Force resisting system moment frames and let's start by considering what will happen if we take a frame designed only for Gravity loading with pinned joints at the ends of all members and we apply a lateral load as we saw when we discussed trusses last week there is no mechanism in place for the perpendicular Force to transfer into the vertical column and thus the frame distorts very easily and collapses it is unstable so how can we make this Frame stable how can we allow this perpendicular force of two Kips to pass through the column and into the foundation one way to do that would be to change these joints to fixed joints and as you can see that's exactly what we do when we create a moment frame that fixed joint allows the lateral Force to transfer down into the column as a Shear Force and that Shear Force also creates bending in the column and so ultimately moment frames resist lateral forces through bending in the columns and you can see how a moment frame will distort under lateral loading compared to how the gravity frame distorted these fixed joints had to remain at 90 degrees and so the columns went into bending so let's consider the behavior of these moment frames up until now we have considered columns as axially loaded Members Only and members with axial loads have an even stress profile over their cross section so typically an efficient axially loaded member will be square in shape but as we learned in week three vending members do not have an even stress profile and vending members actually become more efficient when we increase the depth perpendicular to the axis about which they are bending so now that we are placing bending into these columns how might the shape of our columns change when we use them in moment frames and hopefully by now you're able to answer that question on your own but just to be clear there's a hint now let's look at some math with a quick are example a similar question was actually in your day Zero assessment so if we look at a single Bay moment frame it's very easy to divide up the shear Force into the two columns as long as both columns have the same stiffness the force will be divided evenly between the two columns so with two Kips applied we have one Kip of Shear each in these two columns but what if we add a third interior column well that complicates things a little but that confusion is mostly because lateral forces can be harder to think about than gravity forces if we think about gravity forces first hopefully this becomes a little more clear if we placed an evenly distributed load across this Frame how much would go into the interior columns compared to the exterior columns well for Gravity analysis we would look at tributary areas and we would see that the interior column has twice the tributary area compared to the exterior columns and so if we look at these reactions the interior column will have twice the amount of force compared to the exterior columns and the same rule applies for basic lateral analysis the interior column will take twice as much Shear Force as the exterior columns so now let's evaluate this Frame laterally but let's think about it like we just did in terms of tributary widths and here you can see that we can divide this Frame into four equal spaces and so our total force will be divided four times and we'll end up with V over 4 in each of these spaces and so the amount of tributary force in this exterior column will be V over 4 similarly on the other side will have V over 4.

[00:11:19]but for the interior column we will now be taking both the shear force on this side of the column and on this side and so we'll end up with v over 2.

[00:11:32]so now let's move on to an example with some numbers and let's take this are example here you can see that this example has multiple levels and they even give you the height here but when we're talking about Shear we don't really care about the height nor do we care about the length those Dimensions really only come into play when we start talking about overturning moment for sheer however all we need to do is add up these story Shear forces into a total shear at the second level and so we get one kit plus two plus two is five kips now we take what we just learned to find the base Shear at column two and since this is an interior column we know that it's sheer will be equal to the total five tips divided by two or two and a half tips and so that's it for moment frames in the next video we will be talking about brace frames and Shear walls