A cantilever beam member made from steel with hollow circular cross section experiences an axial load of 300 KN (F1), and a vertical load of 200 kN (F2) as shown in the following figure. The beam is 300mm long and fixed on one end.
We don't see the loading diagram.
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To analyze the cantilever beam member, we will consider the equilibrium of forces and moments acting on the beam. Let's go step by step to find the resulting stresses and deflection in the beam.
1. First, let's calculate the axial stress due to the axial load (F1). The axial stress (σ_axial) in the beam can be determined using the formula:
σ_axial = F1 / A
where F1 is the axial load and A is the cross-sectional area of the beam. Since the beam has a hollow circular cross-section, the cross-sectional area can be calculated as:
A = π * (r2 - r1)
where r1 is the inner radius, and r2 is the outer radius of the beam's cross-section. Please provide the values of r1 and r2 so we can proceed with the calculation.
2. Next, let's consider the vertical load (F2) and calculate the bending moment (M) generated at the fixed end of the beam. The bending moment can be determined using the formula:
M = F2 * L
where F2 is the vertical load and L is the length of the cantilever beam. Please provide the value of L so we can proceed with the calculation.
3. Now, let's analyze the bending stress due to the bending moment (M). The bending stress (σ_bending) in the beam can be calculated using the formula:
σ_bending = (M * c) / I
where c is the distance from the neutral axis to the point of interest (maximum stress), and I is the moment of inertia of the beam's cross-section. For a hollow circular cross-section, the moment of inertia can be calculated as:
I = π * ((r2^4 - r1^4) / 4)
Please provide the distance c from the neutral axis, so we can proceed with the calculation.
4. Finally, to determine the deflection of the cantilever beam, we need to use the appropriate deflection formula for the given loading conditions. Can you specify the type of loading and boundary conditions (e.g., point load, distributed load, simply supported, etc.) on the beam so we can determine the appropriate deflection equation?
Please provide the values for r1, r2, L, and c, and specify the loading and boundary conditions to continue with the analysis.