The Tensor Gage

Abstract

SE V E R A L recent articles (cf., references 1 and 3 and bibliography given there) on the subject of how to determine the complete s tate of strain and stress in a region of sheet from 3 (or 4) strain measurements obtained in different directions indicate the increasing interest of s tructural engineers in the flow of stress through continuous sheets or thin plates under the influence of loads in their own plane. The conventional experimental procedure consists of applying linear strain gages in different directions during three successively repeated load cycles. The expense and technical difficulties of repeating the test load cycle with exactly the same load distribution are obvious where the test specimen is par t of a complicated structure, like an airplane undergoing proof-loading tests. An instrument which simultaneously measures the strain in three directions on the test spot is a great t ime saver. An approach to such a three-component gage with three strain gages mounted in close proximity on a common holder is described in reference 2. Efforts to crowd the elements of a three dimensional strain gage into a small area in order to explore in detail the stresses in the skin of supercharged airplane cabins or in gussets and coherent bulkheads, frames and webs led to the construction of a triangular strain gage. This gage was called the Tensor Gage because it responds directly to the three membrane components of the strain tensor to which the sheet is subjected. This new instrument in effect comprises three 1 in. strain gage mechanisms bu t it engages the specimen a t only 3 points; viz., the corners of an equilateral triangle. This is accomplished by an articulated tripod whose legs are accurately restrained to move only in the direction of the three radii forming a 120° star. The normal length of each radius was chosen 15 mm., which makes the base length of the triangle side 1.02 in. Each tripod leg contacts the specimen surface by means of a sapphire cone having an apex radius of approximately 0.001 in. Each tripod leg is a lever which rocks on a hardened knife edge in a grooveless saddle between accurately positioning thrus t plates with imperceptible friction. The mechanical lever carries a microscopic index reticule in the focal plane of an optical magnification system. A fixed lens projects an enlarged subjective image of the index reticule through a mirror upon a transparent scale which is read through another magnifying glass. The total magnification is such tha t a strain of 1/10,000, which in aluminum corresponds to a linear stress of approximately 1000 lbs. per sq.in., appears as one scale division, fractions of which can be est imated to /± or 1 /5 . Each scale covers 100 divisions. Each index pat tern consists of three differently identified cross lines, 50 scale divisions apart , so t ha t the total range amply covers any test requirement within the yield limits of the structural material. The instrument fastens to the specimen surface quickly by means of a single central suction cup without external clamps. The gage measures l 3 / 4 in. in diameter and 2/2 in. in height and weighs 4 ounces. I t is shown in the accompanying photographs. When applying the gage to test work, readings are taken on all three legs before and after each load step. The differences between successive readings are converted into strain values by means of the following simple conversion formulas: Let a, b, c, be the differences of readings in scale units, before and after the load step. The corresponding strain changes ea, eb, ec, in the directions of the radii of the respective legs A, B, C, are the mean value between t h e