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I have this question I've been attempting and need some guidance. I'm not exactly sure on how to go about this. I'll explain the image I've attached:

This is a gantry crane and it has two hoists along the beam which is $15m$ long. It has two vertical pillars at both ends. I have to assume the beam's weight is UDL (uniformly distributed load) of $1kN/m$ along the length of the beam. I've been told that both the hoists operate at $75kN$. Also, the beam is supposed to behave as a simply supported beam. I'm supposed to calculate the reaction forces applied on the beam by the vertical pillars at either end.

I've attached an image if it makes it more clearer, see it here:

enter image description here

Here's my attempt so far. What's my next step to take? Thank you

enter image description here

Smithy55
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    You need to write two equations: one for translational equilibrium, and the other for rotational equilibrium. What you've do so far is OK. – Fabio Somenzi Nov 04 '18 at 21:14
  • The resulting 150 kN acts at center of the two forces at 7 meters not 7.5 meters moment arm. Rest of the work seems OK. – Narasimham Nov 04 '18 at 21:48

1 Answers1

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HINT

We have that

  • vertical equilibrium $$R_L+R_R=75+75+15$$
  • rotational equilibrium $$4.0\cdot 75+ 7.5\cdot 15 +10.0\cdot 75=15.0\cdot R_R$$
user
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  • @Smithy55 From the second one we should obtain $R_R=77.5$. – user Nov 04 '18 at 22:02
  • @Smithy55 There was a typo in the second equation, now it should be fixed. – user Nov 04 '18 at 22:06
  • Alright, thank you. I understand now. I've got RR to be 77.5 and RL to be 87.5. Thank you for taking the time to explain. – Smithy55 Nov 04 '18 at 22:08
  • @Smithy55 You are welcome! To practice you can try to solve writing the second equation with respect to the right colomn or with respect to the midspan. – user Nov 04 '18 at 22:10