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Unformatted text preview: Equilibrium and Trusses Equilibrium and Trusses ENGR 221 February 17, 2003 Lecture Goals Lecture Goals • 64 Equilibrium in Three Dimensions • 71 Introduction to Trusses • 72 Plane Trusses • 73 Space Trusses • 74 Frames and Machines Equilibrium –Problem Equilibrium –Problem Determine the reactions at A and the force in bar CD due to the loading. Equilibrium –Problem Equilibrium –Problem Draw the freebody diagram of the main body. 1 o 6 in. tan 26.565 12 in. θ = =  R Ax R Ay T CD θ Equilibrium –Problem Equilibrium –Problem Look at equilibrium ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 o x Ax CD o Ax CD o y Ay CD o Ay CD cos 26.565 125 lb cos 26.565 125 lb sin 26.565 40 lb 60 lb 80 lb sin 26.565 20 lb F R T R T F R T R T = + + = =  + = + + = =  ∑ ∑ Equilibrium – Equilibrium – Problem Problem Take the moment about A R Ax R Ay T CD θ ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 o A CD o CD CD cos 26.565 6 in. 40 lb 4 in. 60 lb 8 in. 80 lb 12 in. cos 26.565 6 in. 320 lbin 59.628 lb M T T T = = + =  =  ∑ Equilibrium – Equilibrium – Problem Problem Take the moment about A R Ax R Ay T CD θ ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 o Ax o Ay 59.628 lb cos 26.565 125 lb 71.667 lb 59.628 lb sin 26.565 20 lb 6.667 lb R R =  + =  =  = Equilibrium in 3Dimensions Equilibrium in 3Dimensions In two dimensions, the equations are solved using the summation of forces in the x, y and z directions and the moment equilibrium includes moment components in the x, y and z directions. x y z 0 0 F F F = = = ∑ ∑ ∑ x y z 0 0 M M M = = = ∑ ∑ ∑ Trusses Definition Trusses Definition Trusses are structures composed entirely of two force members . They consists generally of triangular subelement and are constructed and supported so as to prevent any motion. Frames Definition Frames Definition Frames are structures that always contain at least one member acted on by forces at three or more points. Frames are constructed and supported so as to prevent any motion. Frame like structures that are not fully constrained are called machines or mechanisms. Truss Truss Planar Trusses  lie in a single plane and all applied loads must lie in the same plane. Truss Truss Space Trusses  are structures that are not contained in a single plane and/or are loaded out of the plane of the structure. Truss...
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