0
$\begingroup$

I am trying to optimize the angles alpha and theta, for which members of truss would carry the less loads. Given is location of force and value of force.

Problem is, that I get contradictory equations, where decrease of one angle is favorable for one member but unfavorable for other one (as more vertical member gets, more vertical loads it will carry). So I came up with the equation, but I am unable to solve it for angles to get minimum force values in the members.

On one hand, I know that it has something to do with derivatives, because if we set derivative of force with respect to angle to zero, I think one should be able to get the most efficient angle. But, there are 2 equations and I am not sure if this approach is correct or how to set up derivative equation.

Any ideas you may suggest?

Thanks.

I am attaching the drawing of the truss structure below

enter image description here

Improve this question
$\endgroup$
6
  • $\begingroup$ I assume $L_1$ and $L_2$ are constants? or is the length of the rods constant? $\endgroup$
    – NMech ♦
    Jan 15 at 15:22
  • $\begingroup$ I changed the task and refined it a little bit. What is given is $ L_{3} $ and $ F $ , idea is to find optimal angles with absolute value of $ F_{AB} + $$ F_{BC} $ is minimum. $\endgroup$
    – Akhvlediani
    Jan 15 at 17:07
  • $\begingroup$ Is also H constant? $\endgroup$
    – NMech ♦
    Jan 15 at 17:17
  • $\begingroup$ No, $H$ is the height, which is defined by the angles and $L_{3}$ as shown in equation 3 in the Geometry part of the Figure attached. Only known quantities (constants) are $F$ and $L_{3}$, angles are to be found and all other geometries, as well as internal forces in members are defined by angles. $\endgroup$
    – Akhvlediani
    Jan 15 at 17:50
  • 1
    $\begingroup$ It's an underconstrained solution, you'll minimise the axial forces by maximising H, ad infinitum. Both will tend to F/2. $\endgroup$
    – Greg Locock
    Jan 15 at 21:59

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.