# Replace the force and couple moment system acting on the beam by an equivalent resultant force

Obtain resultant forces and moments for equivalent systems. Evaluate distributed loadings intensities. Equivalent systems 1) The overhanging beam is supported by a pin at A and the strut BC. Show that the loading conditions below are equivalent by replacing the loadings by a single resultant force and a moment at A. 1

Question: Replace The Force System Acting On The Frame By An Equivalent Resultant Force And Couple Moment Acting At Point A. 180 N 100 N 1.5 M 04m+ 09m 200 N 0.6 M

Given:A 2D force and couple system as shown. Find: The equivalent resultant force and couple moment acting at A. Plan: 1) Sum all the x and y components of the two forces to find F RA. 2) Find and sum all the moments resulting from moving each force to A and add them to the 45 kN m free moment to find the resultant M RA.

A force system consists of a clockwise couple of 480 N·m plus a 240 N force directed up to the right through the origin of X and Y axes at θ x = 30°. Replace the given system by an equivalent single force and compute the intercepts its line of action with the X and Y axes.

Solution The equivalent single force FR can be located on the beam AB at a distance d measured from A. d = MRA/FRy = 10.56/50.31 = 0.21 m. Replace the force and couple moment system acting on the overhang beam by a resultant force, and specify its location along AB measured from point A.

Replace the force at A by an equivalent force and couple moment at P. 28 . This structural connection is subjected to the 8,000-lb force. Replace this force by an equivalent force and couple acting at the center of the bolt group, O. 29 . Replace the force and couple system by an equivalent single force and couple acting at point P. 30 .

Equivalent Resultant Force And Couple Moment At O. ... Replace the loading system acting on the beam by an equivalent resultant force and couple moment at point O. 30 ... Replace this system of forces by an equivalent resultant force and specify its location measured from B.

Equivalent force -couple systems Original system of a single force F acting on A. The vector position of A relative to O is r. Original system in the moment plane A force F can be replaced by a parallel force and a couple an equivalent force-couple system acting on a point O Adding up a pair of two equal but opposite forces F at O no effect

Given: A 2-D force and couple system as shown. Find: The equivalent resultant force and couple moment acting at A and then the equivalent single force location along the beam AB. Plan: 1) Sum all the x and y components of the forces to find F RA. 2) Find and sum all the moments resulting from moving each force to A. 3) Shift the FReplace the loading below by an equivalent force and couple moment acting at point O. The Wall AD has forces acting upon it on both sides from the water and the soil. If A is a pin joint with the ground, determine its reaction forces and the tension in cable BC required for equilibrium. Determine the resultant couple moment of the three couples acting on the plate in Fig. 3—29. F3 = = 2001b 4 ft 172 = 450 1b Fl = 200 1b Fig. 3-29 300 1b 172 = 4501b A SOLUTION As shown the perpendicular distances between each pair of couple = 3 ft forces are dl — 4 ft, d2 = 3 ft, and d3 — — 5 ft. Considering EQUIVALENT FORCE SYSTEMS . 1. Replace the force and couple system by an equivalent single force and couple acting at point P. Ans: (a) -0.086i-1.184 kN , 21.6 kN m (b) -270 N, 6885 kN m . 2. Determine the magnitude and direction θ of force F and the couple moment M such that theA couple M and the three forces shown are applied to an angle bracket. Find the moment of the couple if the line of acltion of the resultant of the force system is to pass through (a) Point A, (b) Point B, (c) Point C. PROBLEM 3.87 Three control a ABC exert it the finites shown. Replace fortes an equivalent force-couple