This article proposes to consider the calculation of steps of concrete stairs bent at 180°. The stairs are half wall, half hanging. The first two steps are patterned (inviting), the others run.
To design the steps of the stairs in the plan and calculate the width of the treads and the height of the steps, we will take the most common form of stairs - curvilinear wall with a turn of 180 ° . Let's consider a complicated option, in which the steps are adjacent to the walls on two sides, and the third side is hanging.
Fig. 1
Fig. 2
Fig. 3
Let's complicate the task further and make the first two steps inviting.
Fig. 4
Fig. 5
Fig. 6
So, how to calculate stairs? How to calculate formwork for concrete stairs? The following data are required for the calculation:
1. Dimensions of stairs in plan a, b, c.
2. The height of the stairs h (from the screed on the first floor to the screed on the second floor).
3. Decoration of concrete stair treads (thickness of marble, wood, tiles).
4. The thickness of the floor covering of the first and second floors.
мал.7
Припустимо, приймаємо а = 2120мм (розмір обмежений положенням двері в стіні), b = 2510мм (розмір обмежений довжиною отвору в міжповерхове перекриття першого поверху), з = 1880мм (розмір обмежений шириною отвору в міжповерхове перекриття першого поверху див. мал 7).
Синім кольором з штрихуванням показано міжповерхове перекриття між першим і другим поверхом. Малюємо червоним пунктиром максимально дозволені габаритні розміри наших сходів. Поправку робимо на розмір b, зменшуючи його на 5 см, щоб наші бетонні сходи не торкалися своєю бічною гранню плити перекриття (мал.8 )
Fig. 8
So, the width of the stairs in the plan according to size b becomes 2460 mm. We draw the vertical axis of the stairs, which divides it in half, with a green dotted line. The approximate middle line of the march is shown in gray (see dictionary of stair terms for what it is). We draw the inner side surface of the stairs (it is possible by hand on a millimeter scale, but it is better in Archicad or Autocad programs) using the following recommendations:
Fig. 9
-the geometric shape of the inner side surface of the stairs is best chosen as a circle or ellipse, smoothly connecting it with the first and last steps with the help of arcs or spline curves.
-Minimum march width: for internal stairs - 800 mm, for 2-story buildings - 900 mm, for residential buildings with more floors - 1050 mm, for public buildings - 1350 mm. Maximum march width: for residential buildings - 1400 mm, for public - 2400 mm. In this case, we set the width of the march to 900 mm, and draw an ellipse so that the minimum distance from it to the walls a, b and c is approximately 900 mm.
- we draw the first two steps in shapes to our liking, smoothly combining them with an ellipse (Fig. 9). In Fig. 9, I drew an ellipse in the center in blue, which, in my opinion, perfectly created the shape of the inner part of the stairs. I tried to draw and place it so that the minimum distances from the ellipse to the walls were 900 mm – the minimum width of the flight of stairs. From the leftmost point of the ellipse, I drew a spline curve to create the first patterned step. The second symbolic step will be located on the first one, we will draw it a little later. The border of the first step may slightly extend beyond the dotted red dimension line. The first two steps can be made slightly larger than the others. We draw an arc from the far right point of the ellipse to the last step. The last step can also be made wider. From the last step on the outer side of the stairs, we draw a spline curve - the outer side surface of the stairs. We draw so that the width of the stairwell in the center is 900mm, and 950-1000mm at the edges. Now let's draw exactly the middle line of the march, which in « certain » places should pass at a distance of 450 mm from the central ellipse. " Certain » places are the left, upper and right extreme points of the ellipse. In other places, we orient the middle line approximately in the center of the flight of stairs. The middle line is also a spline curve, it can be drawn manually using a ruler, but faster and more accurately in Archicad or Autocad programs. Now is the time to calculate the number of steps in the stairs and determine the height of the risers. Suppose the height of the stairs is h = 2805 mm (from the screed on the first floor to the screed on the second floor). The floor covering of the first floor is 15 mm tile, and the second floor is 10 mm laminate. We calculate the net height of concrete stairs: 2805 + 10-15 = 2800 mm. We divide the net height of 2800 mm by the average height of the step of 170 mm 2800: 170 = 16.47 steps. We round up to 16 degrees. Then the height of the step is 2800: 16 = 175mm. We calculate the height of the first concrete riser for arranging the formwork of concrete monolithic stairs. Let's say, the finishing of concrete stairs from above – marble (30mm + 5mm glue = 35mm). So the height of the formwork of the first step is 175-35 + 15 (tile) = 155mm. The height of the formwork for the other 15 steps is 175 mm. Now let's calculate the tread width along the middle line of the march. By hand, we put a thread on the millimeter along the middle line, then we straighten it and measure the length. The larger the picture, the more accurate the measurements. According to my measurements in Archicad, it turned out to be 4100 mm. In total, we have to make formwork for 16 steps and 15 treads, and the 16th tread is the screed of the second floor. Therefore, 4100: 15 = 273 mm, this is the width of the tread along the middle line of the march. This value satisfies us, therefore the tread width should be at least 250 mm. If the width of the tread was less than 250 mm, then we would reduce the number of steps by 1. The width of the tread would be greater and the height of the step higher. We begin to draw steps. First, draw the first two patterns - the second on the first (Fig. 10). Their width along the main line should be slightly more than 273 mm. Let's take the width of 347 mm for the first step, and 334 mm for the second. We determine these values intuitively so that the first and second steps look harmonious. Then the width of the other steps along the middle line (4100-347-334): 13 = 263mm. Excellent!
Fig. 10
The next stage is the division of the g-k spline curve into 13 equal sections. It is painstaking work by hand. In Archicad, it will take me a minute. Mark the center of the ellipse with a dot A (Fig. 11).
Fig. 11
We design the steps and the left part of the stairs. We continue the segment g-d to the right and get the base line g-d ’ . We connect point 6 and 5 with the center A line and at the intersection with the base line g-d ’ we get points 6 ’ and 5 ’ . We postpone to the right the segment 6 ’ -5 ’ and we get points 4’,3’,2’,1’. (Fig. 12)
That is, 6’-5’=5’-4’=4’-3’=3’-2’=2’-1’.
Fig. 12
Connecting the corresponding dots (4 ’ from 4, etc.) we get a projection of the steps on the left side of the stairs. And then we draw the right part of the stairs. We continue the segment k-f to the left and get the second base line k-f ’. We connect point 6 and 7 with point A with a line and at the intersection with the base line k-f ’ we get 6 points ” and 7 ”. (Fig. 13)
Fig. 13
We postpone segment 6 ” -7 ” to the left 5 times and we get dots 8 ”, 9 ”, 10 ”, 11 ”, 12 ”. We connect the corresponding dots (8 ” from 8, etc.) and get a projection of the steps of the right part of the stairs. Let's remove unnecessary lines and get picture 14.
Fig. 14
Calculation of concrete stairs is ready! Now let's look at our stairs live.
Copyright belongs to Anatoly Karpov,
to the founder of the company Stairs-A
