Gage factor

Introduction to Strain Gages

Have you ever seen the Birdman Contest, an annual event held at Lake Biwa near Kyoto? Many people in Japan know the event since it is broadcast every year on TV. Cleverly designed airplanes and gliders fly several hundred meters on human power, teaching us a great deal about well-balanced airframes. However, some airframes have their wings regrettably brokenupon flying and crash into the lake. Such crashes provoke laughter and cause no problem since airplane failures are common in the Birdman Contest. Today, every time a new model of an airplane, automobile or railroad vehicle is introduced, the structure is designed to be lighter to attain faster running speed and less fuel consumption. It is possible to design a lighter and more efficient product byselecting lighter materials and making them thinner for use. But the safety of the product is compromised unless the required strength is maintained. By the same token, if only the strength is taken into consideration, the weight of the product increases and the economic feasibility is impaired. Thus, harmony between safety and economics is an extremely important factor in designing a structure.To design a structure which ensures the necessary strength while keeping such harmony, it is significant to know the stress borne by each material part. However, at the present scientific level, there is no technology which enables direct measurement and judgment of stress. So, the strain on the surface is measured in order to know the internal stress. Strain gages are the most common sensingelement to measure surface strain. Let’s briefly learn about stress and strain and strain gages.

Fig. 1

Cross-sectional area, A

σ = P (Pa or N/m2)
A Since the direction of the external force is vertical to the cross-sectional area, A, the stress is called vertical stress.

2

ε1 = ∆L (change in length)
L (original length) Strain in the same tensile (or compressive) direction as theexternal force is called longitudinal strain. Since strain is an elongation (or contraction) ratio, it is an absolute number having no unit. Usually, the ratio is an extremely small value, and thus a strain value is expressed by suffixing “x10–6 (parts per million) strain,” “µm/m” or “µε.”

d0 – ∆d

d0

When a bar is pulled, it elongates by ∆L, and thus it lengthens to L (original length) +∆L (change in length). The ratio of this elongation (or contraction), ∆L, to the original length, L, is called strain, which is expressed in ε (epsilon):

Fig. 1

Internal force

External force, P

1

Stress is the force an object generates inside by responding to an applied external force, P. See Fig. 1. If an object receives an external force from the top, it internally generates arepelling force to maintain the original shape. The repelling force is called internal force and the internal force divided by the cross-sectional area of the object (a column in this example) is called stress, which is expressed as a unit of Pa (Pascal) or N/m2. Suppose that the crosssectional area of the column is A (m2) and the external force is P (N, Newton). Since external force = internalforce, stress, σ (sigma), is:

L

∆L

Hooke’s law (law of elasticity)
In most materials, a proportional relation is found between stress and strain borne, as long as the elastic limit is not exceeded. This relation was experimentally revealed by Hooke in 1678, and thus it is called “Hooke’s law” or the “law of elasticity.” The stress limit to which a material maintains this proportionalrelation between stress and strain is called the “proportional limit” (each material has a different proportional limit and elastic limit). Most of today’s theoretical calculations of material strength are based on this law and are applied to designing machinery and structures.

Robert Hooke (1635-1703)
English scientist.Graduate of Cambridge University.Having an excellent talent especially for...