If, in the above question R = 3 then the truss is:-a)Statically determ...
Answer: d
Explanation: B + R = 7 < 2*J. So, the truss will be unstable.
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If, in the above question R = 3 then the truss is:-a)Statically determ...
Statically Determinate or Indeterminate Truss:
A truss is considered to be statically determinate if the reactions and internal forces in the members can be determined using the equations of static equilibrium alone. On the other hand, a truss is considered to be statically indeterminate if the reactions and internal forces cannot be determined using only the equations of static equilibrium.
Stability of Truss:
The stability of a truss refers to its ability to maintain its equilibrium under the applied loads and external forces. A stable truss is one that remains in equilibrium without experiencing any excessive deformations or failure.
Analysis:
In the given question, it is stated that R (the number of support reactions) is equal to 3. For a truss to be statically determinate, the number of unknowns (reactions and internal forces) should be equal to the number of equations of static equilibrium. In a 2D truss, the number of unknowns can be determined using the following formula:
Number of Unknowns = 2n - 3
Where n is the number of joints in the truss. In this case, since R = 3, the number of unknowns can be calculated as:
Number of Unknowns = 2n - 3
3 = 2n - 3
6 = 2n
n = 3
Therefore, the truss has 3 joints. Substituting this value back into the formula, we can see that the number of unknowns is equal to the number of equations of static equilibrium, indicating that the truss is statically determinate.
However, the correct answer given is option 'D', which states that the truss is unstable. This suggests that the truss is unable to maintain its equilibrium under the applied loads and external forces.
Reasoning:
It is important to note that stability and static determinacy are two different concepts. A truss can be statically determinate but still be unstable. Stability depends on the structural configuration, material properties, and external loads acting on the truss.
In this case, without further information or context, it is not possible to determine the stability of the truss solely based on the given value of R. Additional information such as the arrangement of members, support conditions, and external loads would be required to assess the stability of the truss accurately.
Therefore, it is not possible to conclude that the truss is unstable based on the given information. The correct answer should be either option 'a' (statically determinate) or option 'c' (stable) as the stability of the truss cannot be determined without additional information.
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