Final answer:
To determine the force in member GF and whether it is in tension or compression, equilibrium conditions and material properties are required. The formulas for elongation or compression and force involvement depend on whether Young's modulus or the shear modulus is used. Additional information on the structure and load is needed for a precise calculation.
Step-by-step explanation:
To determine the force in member GF and state whether the member is in tension or compression, we need to consider the equilibrium conditions of the structure the member is a part of. The force of tension or compression in a structural member is the result of external loads, support reactions, and the member's own weight. In the case of member GF, since the net force on it must be zero for equilibrium, any force of tension (which would elongate the member) must be balanced by an equal force of compression (which would shorten the member).
If we are given the maximum tension force (F = 3.0 x 106 N) and the cross-sectional area (r² = 2.46 × 10-3 m²), we can calculate the elongation or compression (AL) using the formula:
AL = (1/Y)(F/A)
where Y is the Young's modulus of the material, which relates stress and strain in the linear range, and A is the cross-sectional area. However, if the question requires calculating force using the shear modulus (S), the relevant formula would be:
F = S(A/Lo)
where S is the shear modulus, F is the applied force, A is the cross-sectional area, and Lo is the original length of the member.
Once the force is calculated, if it acts to elongate member GF, the member is in tension; if it acts to shorten it, the member is in compression. To assist further, additional information such as the geometry of the structure, load conditions, and material properties would be necessary.