How to calculate the radius steps of a concrete porch

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This article provides step-by-step instructions for highly accurate calculation of the radius steps of the porch. You will learn how to properly design a concrete porch and measure the dimensions on the ground. The article provides a universal step-by-step method for calculating any of the indicators of the radius plate.

The entrance to the house with beautiful semicircular steps is the dream of many owners of stone houses. Indeed, this is a spectacular solution that will perfectly fit into the design of the facade, provided that it already has rounded elements – the top of the openings, the roof or just a drawing on the facade. We will tell you how to correctly calculate the steps and create a porch project.

The most common conditions for using concrete for steps:

1. Stone house. This requirement is not only aesthetic – wood and concrete have different shrinkage rates. A concrete staircase in a wooden house will “come off”.
2. Level difference between the slab of the 1st floor and the ground – not less than 300 and not more than 1500 mm.
3. March width – at least 1500 mm. Narrow radius steps are inconvenient to climb.

This design will repeat the filling porch with concrete steps, only the side walls will be turned at 180 °. A significant difference will arise in the method of reinforcement and flanging of the steps.

In order to do everything right, we need a project. The presence of a set of ready-made drawings is a rarity, so we will proceed from the fact that there is only the edge of the slab of a house with external walls and the difference between it and the ground level of at least 300 mm.

Initial data

1. The location of the doorway (entrance) is determined, or the opening exists.
2. Method of device – filling ladder without sides (full segment).
3. The difference between the slab and the ground level is 450 mm (3 steps).
4. Step size – standard 150×300 mm.
5. Platform length – 1800 mm.

At all stages of development and calculation, you can resort to the method of constructing a drawing to scale from a sketch – dimensions are taken from nature and transferred to the drawing. For correct calculation, first of all, it is necessary to determine the points and axes of snapping, from which further dimensions will be plotted.

The first reference is the vertical axis of the opening

Following traditional logic, the vertical axis of the porch coincides with the axis of the opening. That is, the edges of the steps are located symmetrically, at an equal distance from the axis or the sides of the opening.

The second anchor is the extreme point of the site stakeout

Next, you should determine the most important (if not the main) performance indicator of the porch – the length of the site *. It should be large enough for a comfortable passage into the house, taking into account the opening side of the doors (if they open outward). Think carefully about this element before going further on the project – all further parameters will depend on its size. Suppose that in our case 1200 mm is sufficient length.

* Platform – a concrete slab into which the upper (last) step goes

The third anchor is the point of contact of the site with the wall

We will immediately consider the most difficult and time-consuming case – the abutment of steps to the load-bearing wall. In the case of the device of boundary walls on the sides, only the final design stage will change – their application to the drawing.

In our case, these points should be determined based on the realities of the facade. The steps should look organic. Determining the anchoring of these points will give us the second indicator necessary for the calculation – the distance between the points of contact, or the length of the chord of the segment. Suppose this distance is 4200 mm.

Basic sketch of the porch: h = 1200 mm; C = 4200 mm; Rpl = 2440 mm; 1 – wall; 2 – opening

One Formula Accurate Design Method

Based on two indicators – length (h) and width (c) of the site, we can calculate the radius of the site (the last step) by the formula:

• R = h / 2 + c2 / 8h

In our case, the radius of the site will be equal to:

• Rpl = 1200/2 + 42002/8 x 1200 = 600 + 17640000/9600 = 2437.5 = 2440 mm

If the walls have not yet been erected, you can determine the center of the circle and carry out further calculations. Marking is done with a cord fixed in the center of the circle.

However, it often happens that the walls and openings already exist, and the length of the site h significantly different from the radius R. That is, the center of the circle is located deep inside the building and the boundaries of the opening do not allow operating with the full size cord. To determine the points of the circle that lie in the inaccessible zone for the cord, you can use the following technique.

Platform length h is divided into a convenient set of segments (a multiple of the length). In our case (h = 1200) it is convenient to take 6 segments with a step of 200 mm. If we draw lines parallel to the wall through these points, we get 7 segments of a circle with a known height (division step – 200 mm) and radius. This data is enough to calculate the chord length using the previous formula.

The chord length will be:

• FROM1 = v (R – h1 / 2) x 8h1, where h1 – the height of the 1st segment (200 mm). The height of each subsequent segment will be equal to the height of the previous one + 200 mm;
• FROM1 = v (2440 – 200/2) x 8 x 200 = v2340 x 1600 = 1934 mm;
• FROM2 = v (2440 – 400/2) x 8 x 400 = v2240 x 3200 = 2677 mm;
• FROM3 = v (2440 – 600/2) x 8 x 600 = v2140 x 4800 = 3204 mm;
• FROM4 = v (2440 – 800/2) x 8 x 800 = v2040 x 6400 = 3613 mm and so on.

Thus, you can calculate the set of indicators of the length of the chord of the segment FROM and, postponing this distance from the axis in a certain place (position h), find a point on the circle with maximum precision. This will give an accurate outline of the boundaries of the radius of the site, from which the remaining steps can be laid.

Splitting a segment to define points of a circle: 1 – desired points; 2 – opening; 3 – axis of the opening and platform; 4 – wall

In the same way, you can calculate the radius of each step and locate the points of the circle with high precision. Each next radius will be equal to the previous one R + 300 mm (tread length). Transfer of points on the ground is carried out using cords and a plumb line.

This method of professional breakdown is relevant if you plan to create uncoated concrete steps (from a special grade of concrete). It is highly undesirable to make mistakes in this case, since additional processing can worsen the appearance of the porch.

This calculation is universal and valid for any type of radius – steps, slabs, railing. Using the formula given in the article, you can calculate any number of radii and put them out on the ground. In the next article, we will talk about how to implement high-precision calculations, as well as provide an adapted method for creating radius steps..

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