L10 Sizing Steel Elements

Added: 2026-05-30

[00:00:00]so before we jump into sizing steel elements let's quickly talk about some of the common steel shapes that you will find on a typical project and we've already talked about a few of these for example the wide flange section we've talked about pretty extensively in our discussion of bending elements and beams and so just to review wide flange sections will have a nominal depth that's given and the second number will be the weight in pounds per linear foot and wide flange sections are often used as beams columns truss cords and occasionally braces in braced frames next we have hollow structural sections which can either be rectangular or round and for an HSS rectangular section the first two numbers will be their exact depth and width and so unlike wide flange sections which give a nominal depth meaning that the actual depth may be a bit larger or a bit smaller than this number given for hollow structural sections the numbers given will be the exact depth and width and the final number will be the exact width of the wall all the way around the section similarly for HSS round this first number here is the diameter of the section and the second number is the exact width of the wall third we have steel angles and once again we have exact widths and depths for our first two numbers and the third number is the thickness of the member on both legs and angles typically aren't used as beams or columns however they are commonly used as masonry lintels brick relieving angles and Truss diagonals and finally we have the double angle which is exactly the same as the single angle except now we are giving a fourth number here which is equal to the separation between the two angles and double angles just like single angles can also be used as lintels or brick relieving angles and also they are typically used for the truss chords or the top and bottom members so if we have just a simple truss like this the double angle will be used for these top and bottom pieces and the middle pieces the diagonals will commonly be single angles so now let's jump into sizing steel elements and just like I said before it's important to note that these are very rough guidelines based on empirical data and are not intended to replace the full analysis that would be performed by a structural engineer so let's look at sizing steel columns and let's recall our buckling formula note that we have a variety of variables and constants in this formula so for example this pi squared number will always be the same it's a constant e for steel is also always 29 000 Kips per square inch and that's regardless of what grade of Steel we're using so if we look at a stress strain curve for steel you'll note that we can have different grades of Steel based on the yield strength which may change but the E the slope of the elastic portion of the line will always be the same so the modulus of elasticity the stress over the strain for the elastic portion of the Curve for steel is always 29 000 Kips per square inch and so that e value is another constant in our formula also when we look at the denominator here we can make some simplifications by saying that most steel columns will be designed for this pinned pinned condition where K is equal to one and so that is another constant in the formula and lastly when we look at our moment of inertia back in the numerator of the equation recall that the moment of inertia is equal to the width times the depth cubed over 12.

[00:05:12]and recall that the moment of inertia changes based on which axis we are looking at so if this is the cross section of our column the moment about the x-axis will be BD cubed over 12.

[00:05:29]and the moment of inertia about the y-axis will be equal to DB cubed over 12.

[00:05:37]so we have to pay attention to whether we're looking at a strong axis or the x-axis bending or the weak axis in this case the y-axis bending but all in all we can simplify what we're looking at with this buckling equation by removing all the constants and only looking at the variables that we can control and when we do that we see that we have BD cubed over L squared those are the variables that we need to be concerned with when we are sizing our column we need to choose an adequate size or cross-section of the member according to its length and looking at this equation further it's really the depth that matters the most as that variable is cubed and the height of the member or the length as that is squared the width of the member since it's not taken to any power is not going to have real control over the buckling strength of the column so changing that width isn't really going to change the strength of the column very much that is until the width becomes greater than the depth and then our weak axis would change but really it's only these two variables that really make an impact on the strength of our steel column and so we can simplify further by looking at the depth of the member over its length and so looking at these two variables this length number is typically what we're going to be given and the depth is what we find and so if we can come up with some kind of common relationship between these two variables we can very easily control the buckling strength of the column and so that's where we get these height to depth ratios so if we are given a column height or a length of 12 feet we can very easily select which situation we have and use these numbers to come up with an adequate step for the column but note that these numbers change a bit depending on the section that we're looking at so we can have HSS round columns HSS rectangular columns wide flange sections that are controlled by buckling in the weak axis and wide flange sections that are controlled by buckling in the strong axis and note that as we said before buckling can occur either about the x-axis or the y-axis and so typically it's the Lesser Dimension that controls the strength of the column and so that's why for our HSS rectangular you want to use the Lesser dimension for D in this equation similarly for wide flange sections controlled by weak axis buckling we want to look at the width of the column and whether a wide flange section column will be controlled by weak Axis or a strong axis buckling is dependent on the bracing for that column and we saw that earlier in this course with one of our example problems so if a column that looks like this with one axis clearly being the strong axis and the other being the weak axis if this column were braced at several locations in the weak axis it may actually be the strong axis buckling that controls but typically we don't have that type of situation typically we will have the same unbrised length in both the weak axis and strong axis directions and so most often for wide flange sections it will be this weak axis formula that controls now let's look at an example of sizing a steel column so given a wide flange shape that is 12 feet tall and unbraced in both directions what size section should we choose well given that it is unbraced in both directions we know that the weak axis will control and so our Target length over depth ratio will be equal to 12 to 20.

[00:10:59]something in that range so let's choose the higher end of this range and let's say we have our 12 foot column convert to inches we are looking for the flange width for this weak axis Target so we substitute the flange width for D and this L over D equation and this needs to be equal to 20.

[00:11:36]and so we get an approximate flange width of 7.2 inches and so now all we need to do is look in our shape database for a column that has a flange width greater than or equal to 7.2 inches and if we start at the bottom here for our wide flange sections and then find the flange width column which is here we see that the first section to surpass 7.2 inches is this w 8 by 31 and so that will be the section size that we choose um so we have a W8 by 31 for our section and that has a flange width of 8 inches which is greater than 7.2 and we can check the accuracy of our math by calculating the actual length over depth ratio so length over depth or in this case flange width that is equal to 18.

[00:13:08]and 18 is in fact in our acceptable range and so this section that we've chosen is okay note that if this column has a particularly large load on it this W8 by 31 nabe this W8 by 31 shape may need to be bumped up further but for more typical loads this W8 by 31 will be okay for this 12 foot height