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Can you solve a statically indeterminate truss?
Therefore, there are 4 unknown reactions. The number of members plus reactions is 15, which is larger than 2 times the number of joint. Therefore, this is a statically indeterminate truss. We can solve for the reaction forces, but not the force in all the members.
How do you determine if a structure is statically determinate or indeterminate?
In regards to beams, if the reaction forces can be calculated using equilibrium equations alone, they are statically determinate. On the other hand, if the reaction force can’t be determined using equilibrium equations only, other methods have to be used, and the structure is said to be statically indeterminate.
What is the force exerted by the hinge?
When a mass is on a horizontal surface, the reaction force acts normal to the surface, in the direction of the line of action of the gravitational force exerted by the mass on the ground. In this case, thus, you would expect the hinge to exert a force into the rod, because this is normal to the wall.
How to deal with a point force acting right on the hinge?
A statically indeterminate structure is one where there are more unknowns (constraints, in this case) than there are static equilibrium equations. Usually one has three equations: ∑ F X = 0, ∑ F Y = 0, ∑ M? = 0 (where ? is any arbitrary point).
How to reduce the degree of static indeterminacy?
To get rid of the remaining two degrees of static indeterminacy for both the fixed-base and pinned-base frames shown in Figure 7.1 and 7.2, we must make some additional assumptions about the behaviour of the frame. We need a way to figure out some approximate values for some of the remaining unknown forces in the frame.
Is there a way to solve the hinges problem?
Adding the two additional equations given by the hinges at C and E to the three global equilibrium equations, we therefore have as many equations as we have contraints (5), and can therefore solve this problem by the traditional means. That being said, there is a much easier way of doing this which is entirely hands-on, without computational aides.
When do you not need a hinge on a portal frame?
If the portal frame has pin-ended columns at the base of the structure, as shown in Figure 7.2, then the first storey columns should not have an added hinge because the column will have zero moment at the bottom end, not at the centre of the height. For this configuration, the initial structure (without added hinges), would be 9 ∘ indeterminate.