2b-ex. Statics Examples • Ex.2b.1 • Ex. 2b.2 • Ex. 2b.3 • Ex. 2b.4 • Ex. 2b.5 Back | Index | Next

 Example 2b.1 Moment Equilibrium Given: In an attempt to pull a nail out of a piece of wood, force P = 20 lb is applied perpendicular to the handle of a hammer. A block is placed under the hammer to provide leverage. The hammer pivots (rocks) at Point A. Let L = 10 in., q = 15o and r = 2.0 in. Req'd: Determine the tensile force in the nail before the nail begins to slide (the nail remains at rest so had zero acceleration). Sol'n: Tensile force F can be determined by taking the FBD of the hammer and summing moments about Point A. Taking counterclockwise moments as positive: SMA = –PL + Fr = 0 F = PL/r = [(20 lb)(10 in.)] / (2.0 in.) F = 100 lb Note that angle q is not needed since P is normal to the handle. Applied force P and force of nail on hammer. What forces are missing if this is to be a correct FBD?

 Example 2b.2 Moment Equilibrium Given: A crane is used to move cargo to and from ocean-going ships. The crane is lifting an object of mass M = 1000 kg. Boom AD has length of LAD = 30 m, and mass of mb = 400 kg. The boom is b = 40° from the horizontal, and a = 20°. Angle ABC is a right angle. Req'd: Determine the tension in cable CD. Sol'n: Create a free-body diagram of the boom, including the weight of the boom itself, which is assumed to act at its geometric center. To determine the tension TCD, sum moments about Point A. Click Here to see the FBD TCD = 18.04 kN

 Example 2b.3 Torsion Given: Specifications a lug-nut require that it be tightened to a torque of 150 ft-lb. Req'd: Using the lug-wrench shown, determine force P to obtain the required torque. Let a = 9 in. Sol'n: The forces P at the ends of the wrench arms cause a torque at Point C of TC = P(2a), which acts about the CD axis. From a FDD of shaft CD, the torque at C must equal the torque at D: TC = TD P(2a) = 150 lb-ft P = 150 lb-ft / (18 in.) = 150 lb-ft / (1.5 ft) P = 100 lb Lug Wrench FBD of lug wrench shaft.

 Example 2b.4 Beam Given: An I-beam shown is acted upon by a 4 kN point load 4 m from the left end. Req'd: Determine the shear force and bending moment distributions throughout the beam. Plot the results on Shear and Moment Diagrams.