Stair calculation (basic, straight, inches)

in this video I'm going to walk you through the steps of a basic stair calculation this calculation is going to be in inches this basic stair calculation is a straight set of stairs a single flight from one elevation to another from one floor to another just a straight line or from one floor to a landing it also works that way so let me show you what I have here set up around the desk here here I have the top of the desk marked as landing I want a set of stairs built here in the middle of the classroom to this elevation from the floor below there it's going to be three or four steps or so and I also have something else in view there this is going to be what's called a trapped run for the run of the stairs you can see in the distance where I put the erasers and the garbage can there's a whole way the garbage can is in this imaginary hallway the set of stairs I'm going to start here at the top of the landing or this is why you take your first step down and maybe 2 or 3 star is 2 or 2 or 3 more steps I don't know how many and it's got the last step is going to be before the hallway and that's how the my set of stairs is gonna meet the opening there in the wall to go into the hallway no part of the stair may go into the hallway so this is what is called a trap to run a trap tron calculation is very very similar to a calculation without a trap front I just want to show you the two skills in one because it's really really not much more calculated than a single set of stairs so I'm gonna explain the terminology of stair building as we go along you need to measurement for this situation the first measurement is going to be a vertical measurement here you have to measure the height of the landing here and in this case this measurement is 25 and a half inches another measurement here is taken horizontally but just because it's just trapped it's a trapped run if it isn't in your case in your situation at home say from a deck somewhere and an exterior set of stairs out in a garden where it's not a trapped runt and don't worry about it but in this case I'm going to take a measurement and this length is 35 inches now I have two measurements taken on site and I can do my stair calculations from here on and just set the camera and let's go I have what was called a total rise the total rise was the difference in elevation from the floor to the top of the deck or top of the landing this total difference in elevation is called the total rise and in our case that was 25 and a half inches the second measurement I took is called total run and in our case it was exactly 35 inches I haven't mentioned it yet but there's one more skill that you need to use to do this calculation you need to be able to convert fraction from fraction format to decimal inches and back fluently somewhere here I'm going to insert a link I have another clip where I demonstrate those skills in this video I'm not going to walk you through those steps I'm just going to demonstrate I'm just going to use the skills themselves to go from fractional format to decimal format without a lot of explanations but if you need to refresh yourself I'm gonna put a link here so I also need one or two more numbers and I'm gonna explain my next number that I'm gonna use is called desired unit price and in my case it's going to be 6 inches what this means is that I want to be my unit rise to to be 6 inches every step the height of every step I want around 6 inches that's a convenient height to lift your foot when you take one step another and another and as you go up to a total elevation of twenty-five and a half inches six inches is a convenient nice number for a casual set of stairs so that's what's meant by units rise the unit being each and every single step one and then the next one and then a third one and maybe a fourth one I don't know so that's what's meant by unit rise and that's why it's desired because we need to we need to see how many of these six inches can be fit into the twenty five and a half inch total rise so what we need to do is divide that number by that number but like I said you cannot enter into the calculator 25 and a half in fractional format I'm just going to convert it right away to twenty five point five now we can divide that number by six but many inches by that manages to get the number of steps number of steps that we are going to take six inches at a time to get to a full elevation of twenty five and a half inches twenty five point five divided by six 4.25 4.25 steps now right away 4.25 we have a problem with that number because you cannot have within normality 4.25 or four and a quarter steps if this has to be a whole number you either take four steps to get up to this elevation or you have to take five steps to get up to this elevation now think about it if you decide to take four steps that means that your original desired unit rise is going to have to be bigger because four steps for bigger steps will take you up to twenty five and a half inches or you can choose to take five steps but in that case five smaller steps than six inches will take you up to the full height of twenty five and a half inches so both of these are okay just as long as you are aware that with more steps you're going to have smaller unit Rises which is fine it's going to be more convenient but if you feel strong and powerful you can go with four steps and take a little bigger steps than six inches in this case I choose to go with four inches we have a another div we have another division to do now because the 25 and 1/2 inches of total height needs to be divided into four equal parts we didn't know in the beginning whether it's going to be three steps four steps five steps or what but now that I have the unit the desired units rise I know it's going to be four steps I'm going to go with four steps let's see what the actual units rise is going to be actual unit rise I'm going to divide the total rise with the number of steps that I've chosen twenty five point five divided by four equals six point three seven five inches six point three seven five inches and that is a final answer that we are going to lay out with our stair gauges on a carpenter's framing square please notice that you cannot lay out 0.375 inches ease we need to convert it to a decimal form from a decimal format to a fraction format so and this is where I'm not gonna explain it too much I'm just going to do it so I'm just going to subtract the six I have all the decimal digits saved and I want to see 16 and it's going to be C 16 6 16 so that's three eighths of an inch no more explanation on this conversion that decimal number is that many inches in fractional form at six and three eighths I'm good to go there I got one more number to lay out the length of the runs and for this I'm going to draw a picture here with my deck or landing in it that's where I started at the landing and that's where my and that's how my steps are gonna be six inches at a time here is my first step second step third step forced that fourth step mayor and my stair stringer is gonna have this shape here this piece is what I need to get out of wood as it stands for stringer that's the piece that I need to make for the stairs it's gonna be looking a little more proportionate okay just work with me on this concept now I have four risers four units rises on this set of stairs and this is gonna be here meeting the floor and then the hallway is going to be here and please notice that with this configuration where the edge of the deck is supporting your stairs finger the number of Rises and number of runs are not identical this is your first run here and the run is a horizontal part of a set of stairs F 1 is your run that's why you place your foot when you go up so that's where you step and then here is your second run and here is your third unit run you see you have four Rises but you only have three runs it's important to notice that you always have one one fewer runs than Rises when the stair stringer and the landing meet in this configuration what that means is that this 35 inch distance has to be spanned equally with three steps so what I need to do is divide 35 inches into three equal portions whatever my whatever my desired unit run would be easy relevant I only have thirty five inches of space and that's what I'm gonna have to work with let's divide 35 inches by three parts thirty-five inches into three part that means every step is going to be 11 point 66 inches long and this is going to be my actual unit run eleven point six six six six inches long and it is a non terminating repeating infinite decimal it's going to be a problem laying it out and I need to convert it into fraction format so that's 11 inches I'm just gonna I'm just going to subtract the 11 so I have all the decimal digits and I want to see sixteenths of an inch so that's going to be ten point six I'm going to round it up to 11 so I have 1116 please note that this 1116 is approximate and is rounded up if you place your starid gauge at the 11 inches and 11 16th spot it's gonna be a little too long because the actual measurement is ten point six sixteen now ten point six 16th I wouldn't entirely call it a normal fraction but you get it that it's gonna be a little less than eleven sixteenth so just keep that one in mind for accurate layout we need to do one more calculation and that's only for the layout this number here and this number here we're good to go to place our stair gauges on our framing square and more calculations to go is called the unit bridge the unit bridge is measured here between one unit rise and one unit of run we have one unit bridge what we need to do is this is an a square d square C square situation here we have the unit rise we have the unit run we have to calculate and do a little square root business to get the unit bridge go back to previous number and I need to enter the amounts in decimal format six point three seven five squared minus plus the number was eleven point six six six eleven point and I want to fill the screen with sixes to be as accurate as possible I can as possible Square on equals were not done we're square rooting this one and on this calculated second function square root equals that's the number we need thirteen point twenty nine I'm just going to leave it on the display the unit bridges thirteen point 29 inches and I do not want to convert this one into inches and fractions of an inch because I do not need the single unit which I want this triple Eight's right away and I'm going to explain it in a second times three equals that number thirty nine point eight eight and I don't want to write this one down too much either I need a fraction out of it so I'm going to subtract the thirty-nine again I have all the decimal digits saved I want to see sixty and seven inch that's close enough to fourteen sixteen is close enough to seven eighths of an inch it's going to be thirty nine and seven eight I tripled the unit bridge because to stay on track with the star layout when this stair stringer is on a piece of wood and lay out the zigzag lines and the piece of wood is looking like this before we cut it off okay I need this first unit bridge and a second unit bridge and the last unit bridge to be laid at accurately I need three unit bridges because I have three runs and the first order of business is to pick a spot somewhere on the stair stringer and lay out this measurement in one length so when I place my stair gauges or and framing square set for these measurements along the edge of the wood I can tweak it a little bit because the wood is never too straight the edge of it is rounded you will see it in the stair layout video it's a little bit problematic these two reference points here will help me stay on track so that my actual pencil line on the piece of wood before I cut into it is not too long it's not too short but is as close as possible to the actual calculations and the actual mesh measurement particularly that we have some rounding here in these calculations okay so that's why we need to triple that one and if I had 14 runs on this set of stairs I would need to times it by three to make sure that every third every third little zigzag line is in its place and I would need to also times it by 14 to make sure that the total run the total not run the total bridge length is also as close to mathematically correct as possible okay so now we are set to go with our numbers we can lay out our stair on a piece of 2 by 10 or 2 by 12

Channel: apprenticemath

Views: 317,386

Rating: 4.5800295 out of 5

Keywords: math, trades, apprenticeship, metal fabrication, carpentry, home renovation, trapped run, stair stringer, total rise, total run, unit rise, unit run, unit bridge, total bridge, Pythagorean Theorem (Concepts/Theories), convert fractions to decimals, landing, flight of stairs, elevation, deck building

Id: n8pczZ9C37E

Length: 18min 54sec (1134 seconds)

Published: Fri Jul 19 2013