In building a structure, we want it to be strong enough and stiff enough to resist all expected forces.
Since most building material has the capacity to flex before it breaks one must consider how to control that flexibility or deflection…the primary examination for most buildings is for deflection. A quote from forum contributor Don_P on two key items of structural concern.
Strength is a life safety issue, it is a "must".
Deflection is a serviceability issue, it is a "may". Things like cracked drywall, opening trim, planes out of plumb, excess vibration (may occur). These are qualitative things rather than safety issues… (but are still important and need to be considered)
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Deflection ConceptsDeflection: is the bending from the original position of an element when a load is applied.

Typical Elements of residential construction: Beams, joists, rafters and studs.
Loads can be: from its own weight but usually it is referenced as the added load.
Typical added loads: Snow, wind, people, or stuff like cows and waterbeds.
Deflection is determined by many items, key items are how load is distributed or applied to the beam or element.
Point Load

Uniform Loading

Progressive Load

Deflection will also be influenced on how the beam is supported.
This shows the beam is able to pivot across the end supports
Beam simple cow

This shows the beam is fixed by a bolted plate and not able to pivot across the end supports – it has slightly less deflection
Beam fixed ends cow

A cantilevered beam with a point load

A cantilevered beam with a progressive load, in this case the designer puts the lighter cows the furthest from the end connection…perhaps anticipating a higher stress at the connection; the designer also increased the connection plate size.

There can be many combinations of end supports, each affecting deflection; this shows a fixed and a pivot.

Deflection will also be influenced by:
The material of the beam such as wood or steel
The shape of the beam such as square, rectangle or I shapes
The size of the beam - most consideration is given towards the depth (tallness) of the beam
Loads can act in any direction, for instance wind can push horizontally on a wall or upward on a roof truss or even by suction.
The deflection concept is quite old with documented concepts and pictures from DaVinci with improved concepts by Galileo as shown in his classic picture.

The more correct mathematical formula was created in the 1750s and is still used today.
Engineers by their focus of education are associated with mathematically solving beam deflection. Some builders by their focus of experience are also associated with solving beam deflection. Most oversight jurisdictions allow a “non-engineer” to calculate beams or other load bearing assemblies if the structure is under a certain size.
Before you decide about one person or another… it has been my experience that both have also made some tremendous blunders.
The picture below is not from a third world country and it was designed by “engineers”.

This one was produced by builders…perhaps for their own use.

Experience would be the deciding factor in selection of either trade.
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How much is too much for beam deflection – wind on a bridge will create deflection…this seems quite large.

Rather than referencing a certain distance of deflection… a ratio of calculated deflection and span length is commonly used as a reference. Written a number of ways: D/L, D over L, D:L, Dead Load/Span Length (DL/L), Live Load (LL/L), Total Load (TL/L), or Delta D
For residential houses one of the key points (see opening paragraph) is to avoid cracking by reducing deflection. Items of concern are brittle finishes such as drywall joint compound, plaster, grout and masonry. Glass is another obvious item I’ll mention later. Many tests have been done in an attempt establish a standard ratio but since most structures are from many “assemblies” we assign different ratios to different assemblies. Restating: this ratio is the deflection from load in relation to the span distance. The chart below (from typical building codes) gives minimum ratios per type of assembly. I’ll discuss missing reference notes in a later post.

As an example a hypothetical floor with:
a span of 360 inches max deflection is 1 inch
or 180 inch span max deflection is ½ inch
or a 90 inch span max deflection is ¼ inch
or a 45 inch span max deflection is 1/8 inch
More information in my next post…