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Q: I was looking over our copy of the engineer's calculations last weekend, but it seemed like they were written in a foreign language. Is there a glossary somewhere to tell me what all these terms and/or symbols mean?
A: The following list may be of help to you. Remember that one of the main activities of engineering is the discovery, attribution and distribution of force throughout a structure. It will not be surprising then that most of the terms you saw are shorthand expressions for some type of force.
Terms : Kip, Moment, Reaction, Shear, Modulus of Elasticity and Fiber Stresses.
Kip :: In the English system, we use pounds to describe weight and feet or inches to describe distance. You may remember that 2000 pounds is called a "ton", but did you know that 1000 pounds is called a "kip"? [It was most likely shortened from "Kilo-Pound"] So, when you see a notation like "kpf", think "kips per foot". 0.48 kpf would be equal to 480 pounds per foot. Engineers use kips since it makes the numbers much easier to work with (especially in the days of slide rules) and reduces errors caused by lost zeros.
Moment :: A way of describing a force acting at a distance. A teeter-totter is a good example. You (the 160 lb. adult) take your child (40 lbs.) down to the park. You put your child on the seat which is resting in the tanbark, then you walk to the other end to get on. Let's assume that the seats are 14 feet apart and the hinge point is fixed at the middle of the board, 7 feet away from each seat. [Think of the hinge like an equal sign.]
| Case #1 How hard will you have to pull down on the far seat to lift your child off the ground? (40 lbs.)(7 ft.) = (7 ft.)(? lbs.) Of course, the answer is 40 pounds. |
| Case #2 Will the teeter-totter balance if you use the standard seat at your end? (40 lbs.)(7 ft.) equals? (160 lbs.)(7 ft.) No, unless you use your legs, your duff is in the tanbark. |
| Case #3 Where would you have to sit on the plank if the teeter- totter is to balance? (40 lbs.)(7 ft.) = (160 lbs.)(x ft.), x = (7/4) = 1.75 feet away from the hinge point. |
In each instance, the units are expressed as "distance" times "force"; foot-pounds of "Moment". When moments are stated, they are typically accompanied by a reference point; a location from which the distance to the acting force is measured. In the above example, the hinge is the reference point. Your child generates (7 feet times 40 pounds) or 280 ft.-lbs. of moment about the hinge, while you generate 1,120 ft.-lbs. of moment. This is the numerical explanation of why you and your child did not balance in Case #2. The calculation of moments is so basic to the engineering process it is required for members, walls, foundations and even entire buildings.
Reaction :: This is a fancy way of referring to the amount of weight an element contributes to a particular location. The "reaction" of a beam on a wall is the amount of load that beam delivers to that wall. If you see a notation like "Rmax.", this is shorthand for the "Maximum Reaction".
Shear :: A type of force which wants to make adjacent materials move past each other. This includes:
When you see the phrase "Lateral Load", this refers to shear forces acting in a direction parallel with the ground surface. The causes of these lateral loads can be wind, retained soil, water, earthquake or impact by an object(s). Stability of a structure is achieved only when lateral loads are properly distributed through the structure, into the foundation and out into the surrounding soils.
Modulus of Elasticity (MOE) :: One of the basic properties of all materials. The MOE is determined by experiment using very sensitive equipment. A measured length of wood is placed in a machine which will attempt to stretch it by pulling from each end. A record is made of the elongation of the wood for ever increasing loads. Given a sufficient amount of data and for loads below that which would cause wood fiber damage, a straight-line relationship between load and elongation can be demonstrated. The slope of this line is the Modulus of Elasticity. Once it is calculated, we can predict the deformation of this material under any given load within the tested (and safe) limits. The greater the MOE, the greater the force required to stretch a given amount of that material. The following is a list of common materials and their respective MOE's:
[ For those of you who might be interested, the formula for calculating deformation is (Deformation)=(P times L)/(A times E) where "P" is the load in pounds, "A" is the cross-sectional area of the member in square inches, "L" is the length of the member in inches and "E" is the Modulus of Elasticity. As an example, a steel bar which has an area of one square inch and is ten feet long, loaded with 10,000 pounds stretches... (10000)(120)/(1)(29000000) = 0.04138 inches.
Another arrangement of this equation may help you understand the MOE better. This is (E) = (P)(L)/(A)(Deformation). The ratio of load over area (P/A) is referred to as the "stress" on a particular material. The degree of deformation, (Deformation/Total Length), is referred to as the "strain" on a material. The equation for the modulus of elasticity is simply the ratio of the calculated stress to the measured strain.]
Fb, Fc, Ft, Fv, Fiber Stress :: Fiber stresses refer to the demonstrated ability of wood to resist forces applied in specific directions with respect to the grain of the wood. Building Codes contain long lists of these allowable stresses for various wood species. Subscripts are used to highlight the force directions under consideration. A short list:
Section Properties : Area, Section Modulus, Moment of Inertia.
Given the forces on a member and the allowable fiber stresses of the material being used, you can determine the minimum acceptable section properties of that member. There are three to be considered: The "Area" of the member, the "Section Modulus" (or simply the "Section") and the "Moment of Inertia" (again, simply the "Inertia"). Subscripts are used when referring to calculated minimums versus actual amounts provided - "r" indicates the minimum required amount and "f" is the actual amount furnished. In your engineer's calculations you may see some notation like "Sf > Sr, ok". This is just a check which shows that the selected member meets the design criteria. The furnished amount should always exceed the required amount.
Ar, Af, Area :: The "area" of any wood member can be calculated by measuring the width and depth at the cut end and calculating that square inch area. The amount of area furnished establishes an upper limit on the reaction a member is permitted to deliver to its support. This maximum can be expressed as (2)(Af)(Fv)/(3) = Rmax.
Sr, Sf, Section :: The "section" of a member limits the strength of the member when subjected to bending moments. For a solid wood beam with a depth less than 12", the section it furnishes can be determined by the following: Sf = (width)(depth)(depth)/(6). Everyone finds the units " inches cubed" a little funny at first, but that will pass. The required section for any member is calculated using the calculated moments and the allowable fiber stresses - Sr = (Moment)/(Fiber Stress). If the moment is expressed in inch-pounds and the fiber stress is expressed in pounds per square inch, the pounds cancel and you are left with inches cubed. All of the mathematics aside, the important word to remember with regards to "section" is the word "strength".
Ir, If, Inertia :: The "inertia" of a member when used with the Modulus of Elasticity of the particular material allows us to predict the deformation (deflection) of that member when loaded. The inertia of a solid wood beam can be determined by the following: If = (width)(depth)(depth)(depth)/(12)...in inches to the fourth power! There are all sorts of complicated formulas for determining deflection under various loading conditions, but these would not be enlightening. What you should remember is that the larger the inertia furnished (If), the smaller the resulting deflection. Or, more simply, inertia is directly proportional to stiffness.
Engineering suffers from its share of technical jargon just like every other profession. Our advantage is that we deal with very tangible elements like beams and walls; things that everyone can relate to. When we speak about forces - gravity, the wind, the occasional earthquake - these too are part of our collective experience. Given a little clarification, anyone can understand engineering methods. I hope this information contributes to your appreciation of the man-made world around you.
Scott McVicker, S.E.