# Math Applications in Construction

Residential and commercial/industrial construction are huge sectors of economy in most countries, with many jobs and careers for skilled workforce. Most construction professionals and even skilled laborers make decent income and have opportunities for growth.  Some students who aim for careers in skilled trades may wonder to what degree mathematics is important to them. Let’s have a closer look and examine some construction sub-trades as examples.

## Math in Excavation

A house cannot be built without foundation! Foundations typically are made out of concrete forms . First, excavation needs to take place. Excavation company expert will calculate the volume of soil that will have to be removed – based on the dimensions and expansion coefficient – and necessary equipment will be determined. Concrete forms will be assembled in a pre-determined shapes and connected together. Their size will be based on the strength requirement for the intended building. A structural engineer will use formulas to calculate what loads are expected, determine necessary strength and dimensions of the foundation based on that.

Once the foundation is in place, the construction of the main structure may commence.

## Math in Framing

Many modern buildings are frame – based. Frames can be made of various materials such as concrete, steel, or wood. In residential construction, wood is used most frequently. To design a house, an architect will use construction codes – rules based on  based on strength and compatibility  of materials – to create drawings. Drawings are complex geometrical designs, where heights, widths, proportions and angles as well as all materials will be inputted to create a n executable plan.

In modern days, special software helps to create drawings and plans, but architects and engineers must be able to use their knowledge and understand/utilize mathematical formulas that go into such calculations. Often, roofs represent more complex shapes in terms of geometry – with various angles, slopes and dimensions combine to give each home a particular look and functionality. Framers are skilled tradesmen and women(ha ha) who will execute the plan relying on their knowledge of geometry and sizing of construction materials. One look at framing square reveals the degree to which math is used in framing!!

## Math in HVAC

Every home and building needs Heating, Ventilation and usually Air-conditioning, or HVAC. HVAC is a specialised subtrade in construction, a very interesting field with a lot of opportunities for those who work in it. It involves math and calculations rather heavily as well!! Lets give you some examples.

To design a heating and cooling system, first, we need to know how much heat the building and every room in it may require to stay warm or how much of it needs to be removed to stay cool. This is determined as “heat loss calculation” and is based on formulas for the type of construction materials and the climate of the geographical area. Then, the heating and cooling system must be able to produce or carry away the heat to match these needs so comfortable temperature range will be maintained within the dwelling, office or commercial space.

The heat for heating is produced by heating equipment which has different capacity. So, the HVAC designer will use heat loss calculation to match it with what equipment (electrical, natural gas etc). Will be used to produce the required amount of heat (same for cooling). Heating energy units and equipment specs all involve numbers that must be understood correctly and converted easily by the HVAC professionals using formulas and conversions.

How do you know how much heat a furnace, or boiler will produce?? Well, a unit of volume unit of natural gas will create so many units of heat when burned! There is a formula for that. But wait , only a fraction of it will be transferred to the heat carrying medium such as hot air. This is called “efficiency” and is described in percentage points.

Frequently, to deliver and dissipate heat to various parts of the building, air ducts are utilized.  And of course we need to know how much warm air needs to travel through the cross section of the duct, under particular pressure, so desired temperature can be maintained! So, volume, pressure, and cross section calculations are all routine part of HVAC system design and installation.

Complicated ? Yes, it is, but it is also a lot of fun.

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