1-126 Section 1 Defining Terms STATICS Equilibrium: A concept used to determine unknown forces and moments. A rigid body is in equilibrium when the equivalent force-couple system of the external forces acting on it is zero. The general conditions of equilibrium are expressed in vector form (∑F = 0, ∑M O = ∑[r × F] = 0) or scalar form (∑F x = 0, ∑F y = 0, ∑F z = 0, ∑M x = 0, ∑M y = 0, ∑M z = 0). Equivalent force-couple system: Any system of forces and moments acting on a rigid body can be reduced to a resultant force and a resultant moment. Transformations of a force-couple system involving chosen points of reference are easy to make. These are useful for determining unknown forces and moments and the critical locations in structural members. Free-body diagram: A method of modeling and simplifying a problem for the efficient use of the equilibrium equations to determine unknown forces and moments. A body or group of bodies is imagined to be isolated from all other bodies, and all significant external forces and moments (known or unknown) are shown to act on the free-body model. FIGURE 1.7.1Accelerometer data from front suspension system of vehicle. Logarithmic decrement ∂ = ln(x 1 /x 2 ); damping ratio ζ = 0.16. ©1999 by CRC Press LLC PLATE 1 Flat-Trac® Roadway Simulator, R&D 100 Award-winning system in 1993. (Photo courtesy MTS Systems Corp., Minneapolis, MN.) PLATE 2 Spinning torque transducer with on-board preamplifier. An angular accelerometer is attached at the center of the torque cell. (Photo courtesy MTS Systems Corp., Minneapolis, MN.) ©1999 by CRC Press LLC PLATE 3 Vibration screening of a circuit board using an electromagnetic shaker and a laser doppler vibration pat- tern imager. (Photo courtesy Ometron Inc., Sterling, VA.) PLATE 4 Vibration patterns of a computer hard disc reader head at 4540 Hz. (Photo courtesy Ometron Inc., Ster- ling, VA.) ©1999 by CRC Press LLC PLATE 5 Vibration patterns of a car door at 40 Hz and 300 Hz. (Photos courtesy Ometron Inc., Sterling, VA.) PLATE 6 Changes in the vibration patterns of a car door caused by the addition of damping material. (Photos cour- tesy Ometron Inc., Sterling, VA.) ©1999 by CRC Press LLC PLATE 7 Detection of delaminations in a foam-and-steel composite plate using vibration pattern imaging. (Photo courtesy Ometron Inc., Sterling, VA.) PLATE 8 Modal analysis of a vibrating turbine blade using Thermoelastic Stress Analysis. (Photo courtesy Stress Photonics Inc., Madison, WI.) ©1999 by CRC Press LLC PLATE 9 Biaxial test setup. (Photo courtesy MTS Systems Corp., Minneapolis, MN.) PLATE 10 Pressure vessel. (Photo courtesy Nooter Corp., St. Louis, MO.) ©1999 by CRC Press LLC PLATE 11 Delta Therm 1000 Stress Imaging System with principal inventor Jon R. Lesniak. R&D 100 Award-win- ning instrument in 1994. (Photo courtesy Stress Photonics Inc., Madison, WI.) PLATE 12 TSA stress images and samples of data processing by Delta Therm instrument (Color Plate 11). (Photo courtesy Stress Photonics Inc., Madison, WI.) ©1999 by CRC Press LLC PLATE 13 TSA stress images showing damage evolution at a weld. Top: beginning of fatigue testing; yellow shows stress concentration at weld toe (no crack); dark blue spots represent lower stress at weld splatter. Bottom: gross and uneven stress redistribution to tips of crack (≈ 0.5 in. long) after 1 million cycles. (Photos courtesy Mark J. Fleming, University of Wisconsin-Madison.) PLATE 14 Direct measurement of crack length and stress intensity factors by TSA stress imaging. Top: crack at 41,000 cycles. Bottom: crack at 94,000 cycles; light shows through the crack; blues show stress relief at crack faces and nearby. (Photos courtesy Mark J. Fleming, University of Wisconsin-Madison.) ©1999 by CRC Press LLC PLATE 16 Strain-gauging of a vehicle’s suspension system in progress. PLATE 15 Closed-loop, electro-hydraulic mechanical testing systems. (Photo courtesy MTS Systems Corp., Minne- apolis, MN.) . Any system of forces and moments acting on a rigid body can be reduced to a resultant force and a resultant moment. Transformations of a force-couple system involving chosen points of reference. members. Free-body diagram: A method of modeling and simplifying a problem for the efficient use of the equilibrium equations to determine unknown forces and moments. A body or group of bodies is imagined to. the vibration patterns of a car door caused by the addition of damping material. (Photos cour- tesy Ometron Inc., Sterling, VA.) ©1999 by CRC Press LLC PLATE 7 Detection of delaminations in a