The absolute maximum shear stress at location A on the surface of the loaded cylinder is approximately 44,328.80 MPa.
To determine the absolute maximum shear stress at location A on the surface of the loaded cylinder, we'll need to use the given values and follow a series of steps. Let's break it down step by step:
Step 1: Determine the applied forces and dimensions
- Given:
- Axial load (F): 7 kN
- Torque (T): 18 kN
- Radius (r): 1.6 cm = 0.016 m
- Length (L): Not provided (Assume the cylinder is infinitely long for simplicity)
Step 2: Calculate the cross-sectional area (A) of the cylinder:
The cross-sectional area of a cylinder can be calculated using the formula for the area of a circle: A = π * r^2.
A = π * (0.016 m)^2
A ≈ 0.000804247719 m²
Step 3: Calculate the normal stress due to axial load:
The normal stress (σ) due to axial load is calculated using the formula: σ = F / A.
σ = (7,000 N) / 0.000804247719 m²
σ ≈ 87,058,823.53 N/m² = 87.06 MPa
Step 4: Calculate the shear stress due to torque:
The shear stress (τ) due to torque is calculated using the formula: τ = T * r / J, where J is the polar moment of inertia.
First, calculate the polar moment of inertia (J) for a solid cylindrical section:
J = π * (r^4) / 2
J = π * (0.016 m)^4 / 2
J ≈ 6.46169617e-08 m^4
Now, calculate the shear stress:
τ = (18,000 N) * (0.016 m) / 6.46169617e-08 m^4
τ ≈ 44,328,759,667.66 N/m² = 44,328.76 MPa
Step 5: Calculate the absolute maximum shear stress at location A:
The absolute maximum shear stress occurs when both normal and shear stresses are acting simultaneously. You can calculate it using the Mohr's circle method:
τ_max = (σ/2) + √((σ/2)^2 + τ^2)
τ_max = (87.06 MPa / 2) + √((87.06 MPa / 2)^2 + (44,328.76 MPa)^2)
τ_max ≈ 44,328.80 MPa