As odd as it seems, engineers sometimes misunderstand the role of material properties. In attempting to solve a problem, they often seek a stronger material without truly understanding which material properties could be used to eliminate problems. Often, using a stronger material does not offer improvement, leaving the engineer dumbfounded.
It is the combination of the properties of the material and the properties of the welded section that determine the behavior of the entire system. Typical material properties that could affect the system include yield strength, fatigue strength, tensile strength, compressive strength, toughness, modulus of elasticity and ductility. Section properties include the cross sectional area, the moment of inertia, the section modulus and the section's torsional resistance.
An old ad, that featured a bow tie and slide rule suggesting that it's probably 60 years old, illustrated the need to understand the fundamentals of material properties. This ad presents a good opportunity to consider the role of the material, and the role of section geometry.
The advertisement proclaimed "At last! For equal weight, magnesium is 18 times as stiff as steel of equal weight. Here's proof." To substantiate the promoter's claim, a demonstration board had been created, comparing the performance of magnesium to that of aluminum and steel. However, the demonstration is flawed and the claim is untrue. Presumably, the demonstration shows that, for equal weight (mass), magnesium deflects less under load than aluminum or steel. The message was that magnesium should be used to obtain lightweight, stiff structures.
A 60-year-old ad claimed to illustrate the need to understand the fundamentals of material properties.
To match the material properties of a magnesium bar measuring 1 inch wide and 0.25 inches thick, an aluminum bar would need to be reduced to a width of 0.66 inches, and steel bar to a width of 0.22 inches.
|Material||Yield Strength||Tensile Strength|
|Typical Value (ksi)||Relative Value compared to steel||Typical Value (ksi)||Relative Value compared to steel|
|Material||Modulus of Elasticity||Density|
|Value (ksi x 10 6)||Relative Value compared to steel||Value (lb/in3)||Relative Value compared to steel|
The typical material properties of magnesium, aluminum and steel are listed in Table 1. The ad claimed that all the bars were 0.75 in. wide. The magnesium bar was 0.220 inches thick. To obtain bars of equal weight (mass), the thickness of the bars was varied. The aluminum bar was 0.137 in., thick while the steel bar was 0.050 inches thick.
The property measured in the ad demonstration was elastic deflection, or "stiffness." As the photo shows, the steel bar clearly deflected further — 18 times more according to the ad's claim. So, pound for pound, is magnesium truly a "stiffer" material?
|Material||Modulus of Elasticity, E (ksi x 10 6)||b (width of bar) (in)||h (height of bar) (in)||Moment of Inertia I x 10-6(in4)||Relative value of I as compared to magnesium||Deflection D (in)||Relative value of D as compared to magnesium|
Standard engineering equations can be used to determine the amount of deflection that occurs when a bar this size is loaded with a 2-pound weight. Table 2 contains the relevant properties and the computed deflection.
The computed values of deflection are similar to those shown in the picture. So, does this prove that magnesium is superior? No. The increased deflection did not result from the change in the properties of the material, but was primarily the result of the properties of the section (e.g., the moment of inertia, I). The thinner steel section (0.050 inches thick) simply flexed more than the thicker magnesium section (0.220 inches thick).
A better comparison could have been made, but was not. Consider a magnesium bar measuring 1 inch wide and 0.25 inches thick. For this comparison, the height will be maintained and the bar width decreased to maintain constant weight (mass). For aluminum, the bar would need to be reduced to a width of 0.66 inches, and steel to a width of 0.22 inches Table 3 captures the relevant properties and computed deflections, with the application of a 10-pound weight.
|Material||Modulus of Elasticity, E (ksi x 10 6)||b (width of bar) (in)||h (height of bar) (in)||Moment of Inertia I x 10- 6(in4)||Relative value of I as compared to magnesium||Deflection D (in)||Relative value of D as compared to magnesium|
In this example, the deflection of the steel bar is essentially the same as that for the other bars, even though the property of the section for the steel bar (the moment of inertia) is actually the lowest of all three. This is true because, contradicting the ad's claim, pound for pound, all of these materials are equally stiff.
The ad demonstrated the importance of the properties of the section, where thinner choices are undesirable. The second example correctly compares the properties of the materials showing that steel is stiffer. For economical designs that require stiffness, even where weight is a concern, engineers should select steel, and then find the property of the section that will control deflection to the specified limits.
Omer W. Blodgett, Sc.D., P.E., senior design consultant with The Lincoln Electric Co., struck his first arc on his grandfather's welder at the age of ten. He is the author of Design of Welded Structures and Design of Weldments and an internationally recognized expert in the field of weld design. In 1999, Blodgett was named one of the "Top 125 People of the Past 125 Years" by Engineering News Record. Blodgett may be reached at (216) 383-2225.