Calculate the force and moment reactions at the bolted base O of the overhead tr

Question

Calculate the force and moment reactions at the bolted base O of the overhead traffic-signal assembly. Each traffic signal weighs 80 lb, while the weights of members OC and AC are 110 lb and 120 lb, respectively. Ans. O_x = 0, O_y = 390 lb, M_O = 5040 lb-ft CW Please explain Do not copy and paste from Wolfram Please handwrite and write quite legibly for everyone to read write very legibly and neatly so that it is easy to read out and understand Do not let the edges of a scanned or pictured image are cropped, resulting illegible scripts Do not skip steps Never use the multiply Symbol (times) between numbers and letters I need solutions and answers as soon as possible. Many thanks

Explanation / Answer

First we will calculate force at O.

Let us assume that the force at O will have two components. Ox ( horizontal component of force or force in the direction of x-axis) and Oy ( vertical component of force or force along y-axis).

As the entire structure is balanced,

Ox = sum of all horizontal forces =0

Oy = sum of all vertical forces

= weight of CO + weight of AC + weight of traffic signal at A + weight of traffic signal at B

= 110 lb + 120 lb + 80 lb + 80 lb

= 390 lb

the direction of Oy is opposite to the direction of all weight ( since this is a balancing force and should be in opposite direction of weight) i.e. +ve y-axis.

Now we will calculate the moment reactions at O

Moment at O = Moment due to OC + moment due to AC + Moment due to traffic signal at A + Moment due to traffic signal at B

= Weight of OC x perpendicular distance between its C.G. and vertical axis through O +

Weight of AC x perpendicular distance between its C.G. and vertical axis through O +

  Weight of traffic signal at A x perpendicular distance between its C.G. and vertical axis through O +

Weight of traffic signal at B x perpendicular distance between its C.G. and vertical axis through O

= 110 x 0 + 120 x 12 CW + 80 x 30 CW + 80 x 15 CW

= 0 + 1440 + 2400 + 1200 lb.ft CW

= 5040 lb.ft CW

ALL THE BEST IN THE COURSEWORK

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