# Let ε < 0.

## 05.16.09

### A stress analysis of a strapless evening gown

Filed under: Dirty, Science humor — Travis @

Effective as the strapless evening gown is in attracting attention, it presents tremendous engineering problems to the structual engineer. He is faced with the problem of designing a dress which appears as if it will fall at any moment and yet actyuall stays up some small factor of safety. Some of the problems faced by the engineer readily appear from the following structual analysis of strapless evening gowns.

If a small elemental strip of cloth from a strapless evening gown is isolated as a free body in the area of plane A in figure 1, it can be seen that the tangential force F is balanced by the equal and opposite tangential force F. The downward vertical force W (weight of the dress) is balanced by the force V acting vertically upward due to the stress in the cloth above plane A. Since the algebraic summation of vertical and horizontal forces is zero and no moments are acting, the elemental strip is in equilibrium.

Consider now an elemental strip of cloth isolated as a free body in the area of plane B of figure 1. The two tangible forces F1 and F2 are equal and opposite as before, but the force W (weight of the dress) is not balanced by an upward force V because there is no cloth above plane B to supply the force. Thus, the algebraic summation of horizontal forces is zero, but the sum of the vertical forces is not zero. Therefore, this elemental strip is not in equilibrium; but it is imperative, for social reasons, that this elemental strip be in equilibrium. If the female is naturally blessed with sufficient pectoral development, she can supply this very vital force and maintain the elemental strip at equilibrium. If she is not, the engineer has to supply this force by artificial methods.

In some instances, the engineer has made use of friction to supply this force. The friction force is expressed by F = f N, where F is the frictional force, f is the coefficient of friction, and N is the normal force acting perpendicularly to F. Since, for a given female and a given dress, f is constant, then to increase F, the normal force N must be increased. One obvious method of increasing the normal force is to make the diameter of the dress at c in figure 2 smaller than the diameter of the female at this point. This has, however, the disadvantage of causing the fibres along the line c to collapse, and, if too much force is applied, the wearer will experience discomfort.

As if the problem were not complex enough, some females require that the back of the gown be lowered to increase the exposure and correspondingly attract more attention. In this case, the horizontal forces F1 and F2 (figure 1) are no longer acting horizontally, but are replaced by forces T1 and T2 acting downward at an angle a. Therefore, there is a total downward force equal to the weight of the dress below B plus the vector summation of T1 and T2. This vector sum increases in magnitude as the back is lowered because R = 2 T sin(a), and the angle a increases as the back is lowered. Therefore, the vertical uplifting force which has to be supplied for equilibrium is increased for low-back gowns.

Since these evening gowns are worn to dances, an occasional horizontal force, shown in figure 2 as i, is accidentally delivered to the beam at the point c, causing impact loading, which compresses all the fibres of the beam. This compression tends to cancel the tension in the fibres between e and b, but it increases the compression between c and d. The critical area is a point d, as the fibres here are subject not only to compression due to moment and impact, but also to shear due to the force s; a combination of low, heavy dress with impact loading may bring the fibres at point d to the “danger point.”

There are several reasons why the properties discussed in this paper have never been determined. For one, there is a scarcity of these beams for experimental investigation. Many females have been asked to volunteer for experiments along these lines in the interest of science, but unfortunately, no cooperation was encountered. There is also the difficulty of the investigator having the strength of mind to ascertain purely scientific facts. Meanwhile, trial and error and shrewd guesses will have to be used by the engineer in the design of strapless evening gowns until thorough investigations can be made.

Condensed from A Stress Analysis of a Strapless Evening Gown and other essays, ed. Robert A. Baker (Prentice-Hall) 1963.