The Whitmore Section
By William a. ThornTon, P.E., Ph.D., anD Carlo lini, P.E.
How to use the Whitmore method for tension and compression strength checks. ANyONE WhO hAS hAD ThE TASk of designing a bracing or truss connection has probably come across the Whitmore section. For most cases, the method is simple and straightforward. However, there are situations where determining the Whitmore section along with the tension and/or compression checks that follow are not quite so clear. This article addresses potential areas of confusion, and provides the reader with background information on the development of this approach. Whitmore 101 First, it’s important to recognize what the Whitmore section is. It is a simple way to determine how force from a brace spreads through a gusset plate. It’s used to make checks of gusset plate yielding and buckling possible. Gusset plates have been used in steel structures since the earliest metal trusses. However, research in the early part of the 20th century regarding the distribution of stresses in gusset plates under tension or compression loading was limited. R.E. Whitmore made note of this lack of knowledge in 1952, providing the following 1941 quote from T.H. Rust, who had conducted earlier tests on gusset plates: “It is difficult to believe that there is a more important or more fundamental problem in need of further investigation in the field of structural engineering than steel gusset plates. They constitute a formidable problem in stress analysis capable of further exploitation in the laboratory…” In an attempt to better understand gusset plates, Whitmore conducted a test on a mock-up of a truss joint connection for a 295-ft truss that was constructed at quarter scale (see Figure 1). Armour T. Granger, head of the Civil Engineering
Fig. 1: Truss outline (Whitmore, 1952). Fig. 2: Stress distribution using Whitmore method (Whitmore, 1952).
Department at the University of Tennessee during that time, had been interested in gusset plate stresses, most likely as a result of his work experience in bridge design while at Ash, Howard-Needles and Tammen. It was upon Granger’s suggestion, and under his supervision, that Whitmore conducted this test. Based on the test results, Whitmore concluded that William A. Thornton, P.E., stresses occurred on the gusset plate as Ph.D., is corporate consultant to shown in Figure 2. AISC member firm Cives EngiThis article focuses on the direct neering Corporation, Roswell, tension and compression stresses on Ga. Carlo Lini, P.E., is an the Whitmore section. It is also imporAISC Steel Solutions Center tant to note that some of the conditions advisor. Prior to joining AISC presented in this article were not tested in 2011 he was a staff engineer by Whitmore, but are what we believe with Ruby + Associates, Farmare reasonable answers to questions we ington Hills, Mich. have received.
MODERN STEEL CONSTRUCTION july 2011
Although Whitmore’s findings were published in May, 1952, widespread use of the Whitmore section did not occur until the late 1970s. In fact, the method was not widely presented to the engineering community until 1974, when it was discussed in Fisher and Struik’s Guide to Design Criteria for Bolted and Riveted Joints. These Days, It’s in the Manual An explanation of how to calculate the Whitmore section is provided in Part 9 of the 14th Edition AISC Manual. A figure is also provided in the Manual (Figure 9-1) to aid the user and is shown here in Figure 3. The Whitmore section is used to determine the peak tension or compression stress of an uneven stress distribution at the end of the joint. It does this by establishing an effective length, which Whitmore determined could be calculated by spreading the force from the start of the joint, 30° to each side in the connecting element along the line of force. The most common application of the Whitmore section is in gusset plates for bracing and truss connections. Figure...