Use the principle of virtual work to determine the vertical deflection and rotation at tip (Point B) of the cantilever shown below. (L=6847 mm, q = 5331 N/mm, M = 1408549 N.mm, and El = 8.6 x 1014 N. mm²) q Y M X A ΕΙ B L Step -1 Let the coordinates defined with origin located at B and x-axis pointing to the Left and Y-axis pointing upward. The bending moment, M (Units: N.mm), in the beam as a function of spatial coordinate x(Units: mm) can be most accurately described by Select one: 1. M=1126839.200 +2132.400*x*x 2. M=-1408549.000 - 3198.600*x*x 3. M=-1408549.000-2665.500*x*x 4. M=-1408549.000-2132.400*x*x 5. M= -1408549.000+2665.500*x*x 6. M= 1408549.000 + 2665.500*x*x 7. M= 1408549.000-2665.500*x*x

A > X L Determine the function for internal resultant moment in terms of x given: L = L Wo = W M(x) = B x³ + Number For: Wo = 6 kN/m L = 3 m Find the variables a, b, c, and d for the equation in the form ax³+bx²+cx+d. Note: terms may be equal to zero M(x) = Number x² + Number Wo x + Number

calculated using a matrix determinant: Part C - Moment due to two forces i j k M =r x F =| rz ry As shown, a member is fixed at the origin, point O, and has two applied forces, F1 and F2, applied at the free end, rz F, F, F point B. (Figure 3) Notice that the order of the elements of the matrix determinant is important; switching rows 2 and 3 of the determinant would change the sign of the moment from positive to negative (or vice versa.) The forces are given by F1 = 115 Ni- 110 Nj+ 55 N k and F2 has magnitude 195 N and direction angles a = 143.0°, B= 57.0°, and y= 75.2°. The dimensions are x1 = 1.30 m, y1 = 1.85 m, and z1 = 1.10 m. What is the moment about the origin due to the applied forces? Figure 3 of 3 Express the individual components of the Cartesian vector to three significant figures, separated by commas. • View Available Hint(s) vec ? Mo =[ i, j, k] N. m Submit В < Return to Assignment Provide Feedback

a = 4 mb = 3.2 mc = 2 mF = {-7i+4j+12k} NSpecified axis: AF Find the following: Find the z-component of the moment of F about the specified axis. Find the x-component of the moment of F about the specified axis. Find the magnitude of the moment of F about the specified axis. Find the y-component of the moment of F about the specified axis.

Review Learning Goal: To use the vector cross product to calculate the moment produced by a force, or forces, about a specified point on a member. Part A - Moment due to a force specified by magnitude and endpoints The moment of a force F about the moment axis passing through O and perpendicular to the plane containing O and F can be expressed using the vector cross product, Mo =r x F. In a properly constructed Cartesian coordinate system, the vector cross product can be calculated using a matrix determinant: As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 1) The force has magnitude F = 180 N and is directed as shown. The dimensions are ¤1 = 0.350 m, x2 = 1.90 m, y1 = 2.30 m, and z1 = 1.20 m. What is the moment about the origin due to the applied force F? i j M =rx F =|rz k Express the individual components of the Cartesian vector to three significant figures, separated by commas. ry F F,…

Required information A rope connecting points A and B supports the force F shown in the figure. Write expressions using Cartesian vector representation for the following. Take L = 8 ft and F= 12 lb. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. y 30° es ÜAB : the unit vector in the direction from A to B. ûAB =

There are no numbers that answer should be symbolic. There should be 2 coordinates that are symbolic.

te F B (0,0,0) <3 of 3 An old wooden telephone pole with a single cross member was blown off center during a recent storm To temporarily stabilize the telephone pole, a repair crew has attached a cable from the end of the cross member to an eye-ring stake anchored in the ground. (Eigure 3) If the origin O of a coordinate system is placed where the pole meets the ground, the point where the cross member is attached to the pole is A(-1.50, 2.10, 23.9) ft and the point where the cable is attached to the end of the cross member is B(-1.50,-2.90, 26.9) ft. The cable's direction is (1.00-1.00-1.00k) and it has a tension of 145 lb. What is M₁, the moment that tends to twist the telephone pole due to the tension in the cable applied at point B? Express your answer numerically in pound-feet to three significant figures. ▸ View Available Hint(s) M₁ = V ΑΣΦ it vec ? lb-ft

An L-shaped bracket is supported by a frictionless pin at A and a cable between points B and D. If pin A is the origin, point C is at (-7, 0); and pin B is at (-7, -10). The cable is attached between point B and an anchor at point D, at (-2, -14). Units are in feet. Force F acts at point C at an angle of 60o from the positive x-axis. Determine the magnitude of the moment that the force F produces about point A. Determine the tension required to hold the bracket in position.

Please solve this