The Misuse Of 1/360

First, what does 1/360 and L/360 mean?

Take L/360. This is part of an equation that is commonly used by structural engineers when designing structural members, especially beams. The full equation is:

the maximum allowable deflection (in inches) = the unsupported span (in inches) of a beam divided by 360 inches.

So as an example: if a beam is 12 feet long, the maximum allowable design deflection is simply 144/360  or .4 inches. 

A deflection ratio of 1/360 is the maximum deflection ratio that is allowed in many applications. The maximum deflection ratio is (usually) 1/360. You might ask where this comes from. When drywall is applied to a wood frame ceiling/floor, it will crack if ceiling/floor t deflects in excess a deflection ratio of 1/360. 

Using the maximum deflection in the example 12-foot beam a maximum deflection ratio can be calculated in this manner:

Deflection ratio = maximum deflection (inches)/span (inches)

.4/144 = x/360 =1/360

The Engineer’s Alice in Wonderland

Why do I say these perfectly legitimate engineering concepts are misused?

Consider that the maximum deflection L/360 and the deflection ratio are legitimately used when beams are being designed. The code used in residential design mandates their use in design. With very few exceptions, the codes do not address how a constructed structure is required to perform.

I can understand why a layperson would believe that a beam designed to deflect no more than an inch when fully loaded would, in fact, deflect no more than an inch when fully loaded, but Professional Engineers should know better. The problem is that the engineering calculations may not reliable estimates in the sense of predicting actual future deflections.

Calculated deflections for steel beams are comparatively reliable. Calculated wood deflections are less so. Calculated deflections for reinforced concrete are less reliable still.  

Consider the following discussion concerning the inability to accurately calculate and predict how much a reinforced concrete beam will sag or deflect when placed under a given load.

Although the research engineer in the laboratory is able to carry out carefully controlled loading tests in which measured instantaneous elastic deflections are within 20 or 30 percent of those predicted by empirical equations for deflection, the practicing engineer must expect deviations greater than 30 percent between predicted and measured deflections, constructed under actual field conditions. Deflections are minimized when beams are carefully constructed out of high-strength, low slump concretes that are well compacted and effectively cured. In the field the engineer has a certain limited control over construction methods and procedures by means of the plans and specifications covering the design of concrete mix and details of placing steel and concrete; however what the designer specifies what the construction crews produce can differ widely. Water content may be increased at the job site, incomplete compaction may leave voids and honeycombing, and reinforcing bars may be improperly positioned. By reducing the quality of the concrete, these and other construction procedures can produce members that will undergo larger than expected deflections.

Consider what the American Concrete Institute (ACI) says about the relation between the magnitude of actual deflection and the calculated allowable deflection in reinforced concrete beams.

It should be emphasized that the magnitude of actual deflection in concrete structural elements, particularly in buildings, which are the emphasis and the intent of this Report, can only be estimated within a range of 20 – 40 percent accuracy. This is because of the large variability in the properties of the constituent materials of these elements and the quality control exercised in their construction. Therefore, for practical considerations, the computed deflection values… ought to be interpreted within this variability.

This statement is from ACI 435R-95 Control of Deflection in Concrete Structures. Reported by ACI Committee 435. American Concrete Institute Box 19150 Redford Station, Detroit Michigan 48219

Why are these calculations poor predictors of performance for concrete beams?

There are several things to keep in mind. Engineers can produce conservative slab-on-ground foundation designs and specifications, but he or she has little or no control over what the concrete crew does at the site. So what can happen in the field?

Excessive water content

The water-cement ratio is a critical indicator of future strength and durability. Concrete requires some water – it serves as a catalyst that results in the cement turning into a durable and strong concrete. Water is added at the concrete plant. Ideally, no additional water is required at the construction site. If water is added, it will eventually result in voids in the concrete as the water evaporates out of the concrete.

In my experience, it is rare for no water to be added at the site. Ten gallons for a truck is common. In some cases, it is necessary to add water to make the concrete more workable. This is usually a result of poor planning. Sometimes it is out of anyone’s control. An example is a traffic jam where the ReadyMix trucks cannot reach the site in a timely manner.  

Incomplete compaction

If the concrete is not properly compacted, there will be excessive honeycombing that will reduce the stiffness of the slab. It is imperative that the concrete in the beams be compacted.

Lack of adequate compaction is common. It is common for the perimeter grade beam to be compacted by tapping the perimeter forms using a sledgehammer. This is better than nothing, but a sledgehammer is a poor substitute for a concrete vibrator.

I’m not sure, but I cannot remember a single instance where the interior concrete beams were compacted in any manner. Lack of proper compaction and too much water is a recipe for inadequate stiffness leading to excessive bending.        

High strength concrete

Most concrete in the Houston area is going to be 2500 psi (pounds per square inch in compression) or 3000 psi concrete. Using a stronger concrete can help compensate for other shortcomings. I have never seen high strength used on a residential foundation. 

Low-slump concrete

Low slump concrete has a higher proportion of cement to water. Low slump concrete is generally better quality and is stronger than high slump concrete. Slump is a field test. In my experience, builders never test for slump.    

Effectively cured

If the concrete is not effectively cured, it may never reach the design strength. There are chemicals available to cure concrete. Spraying the slab surface with water 5 to 10 times per day is very effective and cheap. Curing should take place for at least the first 7 days after the concrete is placed.

As you might expect, I almost never see slab-on-ground foundations being properly cured.   

Improper positioning of reinforcing steel

As a general rule, rebar should have at least 2-inches of concrete cover to protect the rebar from moisture intrusion. If moisture penetrates to the rebar, the steel will begin to rust. When steel rusts it grows in volume and that results in damage to the concrete.          

Forms removed too early

The concrete forms should be left in place for a minimum of 28 days after the concrete is placed. If the concrete is not fully hardened, creep deflection can increase by several hundred percent as compared to concrete that has fully hardened prior to the forms being removed. 

Premature cracking due to early form removal can reduce bending stiffness by as much as 50% or even more.


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