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For a direct stepped rod loaded with a system of longitudinal forces (Fig. 1), where F1 = 25kN, F2 = 50kN, F3 = 30kN, it is necessary to determine the magnitude and direction of the support reaction in the embedment.
An example of calculating the support reaction in the embedment of a straight stepped rod under tension-compression.
Task
Task
fig. 1
Solution example
Solution example
Draw the coordinate axis z coinciding with the longitudinal axis of the rod.
Since under tension-compression all external forces applied to the rod are located along its axis, there will be only one of the possible forces for closing six forces here – the longitudinal reaction R.
In order to write the equation of static, let us give this force an arbitrary direction, for example, to the left (Fig. 2).
fig. 2
We write the equation of equilibrium (immobility) of the rod.
To do this, project all the forces on the z axis, the sum of which should be zero.
Moreover, the forces whose direction coincides with the direction of the z axis are positive, and the forces having the opposite direction are respectively negative:
From here we find the value of the support reaction R:
A positive sign of the reaction R means that the initially chosen direction turned out to be correct.
Solution Verification
Solution Verification
To verify the correctness of the result, you can simply add all the forces directed to the right:
and forces directed to the left (including the support reaction R):
These amounts must match.
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