4. Express the force F as a vector in terms of the unit vectors i, j, and k. Determine the angles Ox, 0y, and 02which F makes with the positive x-, y, and z-axes.2, mmB (-25, 50, 40),F = 750 Nу, тmА (15, -20, —25)X, mm

Answered: 4. Express the force F as a vector in…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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1.2.6
3.) The Force F produces a moment of F+B N•m clockwise at point A, and equal magnitude of moments (in N-m) directed counter – clockwise at point B and clockwise at the origin 0. The Force F acts at point C. Determine the following: a.) The Force F. b.) The coordinate y. Substitute: B=465, C=9, F=2060 y A(0, C). C(6,y) 4 O(0,0) B(6,0) F 3:
1. Determine the Moment due to force F about: a. Point O b. Point B Note: The thickness of the beam is NOT negligible and is given in the image. Y ///// F=225N 9m 3m Th 5m B 2m O
Force F= 2,000 N acts from A towards B. 275 mm A 550 mm 220 mm Determine the moment of the force about point C in N m. (The line of action for F does not pass through O. That illusion occurs due to the isometric drawing. Express your answer in vector form.) N-m Determine the shortest distance from point C to the line of action of the force in mm. mm
2. The force of 462 N is directed from point B to point C. a. Determine the moment that the force makes about a line joining points A and D. b. Use the scalar formulation to determine the moment the force makes about the x-axis. c. Use the scalar formulation to determine the moment the force makes about the y-axis. d. Use the scalar formulation to determine the moment the force makes about the z-axis.
Y. 3. The force system shown consist of a counterclockwise couple of 720 N-m plus a 1200 N force through the origin O, directed down to the left as speçified. Determine the (a) distance between the forces and (b) intercepts of the single force at A(a,0) and B(0, b). 13 12 F=1,200 N A(a,0) X C= 720 N-m A B(0,b) F=1,200 N 200 N 150 N 20 cm 4. Given 3 pulleys, the circular sections of which are concentric, and acted upon by three couples as shown. 300 N 40 cm Determine its resultant moment, 300 N e 3 150 NY 200 N+ 30 cm 100 N 150 cm 5. The force system on frame ABCDE is shown below. Replace the system by a force equal to the resultant of the three forces, acting vertically at B 1sd cm plus a couple acting horizontally at D and E. 100 am D 150 cm 30 N
A. The 370 N force acting on the frame as shown in figure is to be resolved into two components acting along the axis of the AB and AC. Ir the component of force along AC is required to be 600 N. directed from A to C, determine the angle 0 between AB and AC. 370 N
Forces F1, F2, and F3 act at point A. The forces are F1 = (364i + 364j − 364k) N, F2 = (−546j − 409k) N, and F3 = (455i) N. (a) Determine the resultant moment of the three forces about point O. Report your answer as a Cartesian vector in N · m. M0 = ( ) N m (b) Determine the resultant moment of the three forces about point O. Report your answer in terms of its magnitude in N · m and direction angles in degrees. M0 = (N m) αO = βO = γO =
66
11. A, B, C are vectors defined by A = 8i + 2j- 3k, B = 3i-6j+ 4k, and C=2i-2j-k, where i, j, k are mutually perpendicular unit vectors. (i) Calculate A.B and show that A and B are perpendicular to each other (ii) Find the magnitude and the direction cosines of the product vector (AXB)
For the system of forces acting on point O, determine the following: a. the magnitude and direction of the components of the 140-N force when resolved along the v- and x-axes b. the partial resultant, P, of the three known forces c. force F that will be added to P so that the resultant, R, is minimum d. corresponding R
The bar ABC has multiple bends in different directions. It has a force applied at point C. Using the listed parameters, find the resulting moment about A expressed as a Cartesian vector. A LA B. X y C 02 F value units L1 parameter 275 mm L2 L3 L4 400 mm 225 mm 475 mm 70 80 F 60 The moment about point A = }N-m NOTE: Use i, j, k for i, j, k

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4. Express the force F as a vector in terms of the unit vectors i, j, and k. Determine the angles 0,, 0y, and 0, which F makes with the positive x-, y, and z-axes. 2, mm В -25, 50, 40). F= 750 N у, тm А (15, -20, -25) X, mm