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Calculate the horizontal and vertical components of the reactions at the supports.

I found the horizontal force for the pin by adding the forces to 0 and I know I can find the vertical reaction of the pin by summing the forces in the y direction. But I get stuck on what do do to find the vertical reaction at the roller support which I need to calculate the vertical force at the pin. If I did a moment calculation at the pin do I count the 10kN force at the top?, don't you only count the stuff that's only in a straight line from the place you're calculating the moment from?.

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  • $\begingroup$ Does the block have a mass or is it massless? $\endgroup$ – Karlo Mar 3 '16 at 8:18
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    $\begingroup$ Yes it is massless and the angle is 45 where the 10kN is. $\endgroup$ – Gustav Magnusson Mar 3 '16 at 8:40
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    $\begingroup$ Yes you need to include the 10 kN force in your moment calculation because it's line of action does not pass through the pin (since you are taking moments about the pin). $\endgroup$ – atom44 Mar 3 '16 at 9:17
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You don't always have to use moments to calculate reactions. In this situation it's possible just by balancing horizontal and vertical forces.

You have one force at an angle. With all our reactions at right angles, you should convert this force into it's two resultants (7.1kN in both the vertical and horizontal direction).

There is only a single horizontal reaction so this must solely resist the 7.1kN horizontal load. Therefore this reaction is 7.1kN.

The other force is 7.1kN upwards. You can proportionally divide this between the two supports, as we know that the closer support will take more of the load. The proportion would simply be 3/4 to the pin and 1/4 to the roller as we know the distances.

Dividing 7.1kN into these proportions means the rollers vertical reaction is 1.76kN downwards and the pin is 5.33kN downwards.

As a final check, taking moments around any point will give a result of 0 which is correct.

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Take

  • Sum of horizontal forces: horizontal component of the 10 kN force and one horizontal reaction force.
  • Sum of vertical forces: vertical component of the 10 kN force and two vertical reaction forces.
  • Sum of moments around left support pin (dashed lines in following picture). There is a contribution by the 10 kN force (project it perpendicular to the connection line between its point of action and the left support pin) and a contribution by the vertical reaction force in the rolling support (right).

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