Chapter 4, Problem 129P

The design specifications for the attachment at A for this beam depend on the magnitude and location of the applied loads. Represent the resultant of the three forces and couple by a single force R at A and a couple moment. Take: M 25 kN .m ;a = 30 ; x = 1.6.m 4 kN 2 m -1.5 m- -0.8 m 2 kN 3 kN

Replace the force and couple moment system acting on the system by a single resultant force and specify its location along the horizontal beam measured from point O. Be specific as to where the resultant force is pointing (i.e. provide an angle and quadrant).

Replace the two forces with an equivalent resultant force and couple moment at point O. Let F = 20 lb.

Replace the three forces acting on the rectangular solid with a wrench. Specify the magnitude of the moment Massociated with the wrench. Enter a positive number for M if the wrench acts in a positive sense, enter a negative number if it acts in the negative sense. Specify the (x,y,z) coordinates of the point P in plane ABCD through which the line of action of the wrench passes. Illustrate the wrench moment and resultant in an appropriate sketch. 25 N 95 mm. Answers: M= y= 55 mm, 29 40 mm 20 N 110 mm. B N-m mm mm mm 35 mm 30 N

Replace the two forces acting on the rectangular solid by a wrench. Write the force R and moment Mas vectors and specify the coordinates of the point Pin the x-y plane through which the line of action of the wrench passes. 240 mm 450 mm 160 N 160 N 360 mm Answers: R= (i it j+ i k) N M-( it j+ i k) N-m Coordinates of point P. (ху) - ( )mm

d= 3.8m (on the figure of the beam) Determine the equivalent resultant force and determine the equivalent couple moment at point O.

heplace the force and couple-moment system acting on the plate by a single resultant force. Specify the coordinates (x, V. 0) through which the line of action of the resultant passes. F1 = 10 lb 4 ft 4 ft F2=50 lb 50 Ib - ft FR = %3D +32 y = Ilok

3. Determine the moment of the equivalent force-couple system of the following figure at point A (F₁ = F₂ = F3 = 500 N) Answer: MA=

The pipe assembly is subjected to three forces of F1 = {3.00, 4.00, -2.00} kip, F2 = {0, 0,-4.00} kip, and F3 = {-3.00, 0, 0} kip. Determine the sum of the moment of the forces 1) about x-axis (the unit vector of x is i) and 2) about line AC. Express the result as a Cartesian vector.