A rod with variable diameter d and 2d is fixed at both ends and subjected to moments \(M_0\) and \(3M_0\) as shown in the diagram below. Plot the bending moment diagram, plot the maximum shear stress diagram \(\tau_{max}\), and calculate the angle of section C rotation \(\varphi_C\). Given numerical data: l=1m, d=5cm, \(I_0=1000 cm^4\), G=80 GPa

What stresses will occur in the double-ended supported and loaded stepped shaft AB as shown in the figure? Data: G = 60 GPa, dw = 4 cm, dz = 8 cm, d = 7 cm.

Measure the diameter of the rod twisted by a torque of 30 kNm, if the torsional strength is \(k_s=70 MPa.\) Calculate the stresses that will occur in this rod, draw a diagram of the torsional moments and the angle of twist. Data: G = 80 GPa.

Measure the diameter of the rod twisted by a torque of 20 kNm, if the torsional strength is ks = 70 MPa. Calculate the stresses that will arise in this rod, draw a graph of torsional moments and angle of twisting. Data: E = 215 GPa, \(\nu =0.3\)

Calculate the stresses that will occur in this rod, draw a graph of twisting moments and angle of twist. Data: D = 25 cm, d = 20 cm, G = 80 GPa.

Measure the diameter of the rod being twisted by a torque of 40 kNm, if the torsional strength is ks = 70 MPa. Calculate the stresses that will occur in this rod, draw a graph of torsional moments, shear stresses, and angle of twist. Data: G = 80 GPa.

Calculate the maximum angle of rotation of the rod shown in the drawing. Data: D = 10 cm, d = 5 cm, G = 80 GPa.

What is the maximum bending moment M that can be applied to a shaft with diameters dz = 8 cm, dw = 4 cm, d = 6 cm, if permissible stresses are 120 MPa? G = 50 GPa.

What is the maximum torque M that can be applied to a shaft with diameters dz = 8 cm, dw = 4 cm, d = 6 cm, if the permissible stresses are 120 MPa? G = 50 GPa.

Task content A rod with a circular cross-section with a diameter of \(d = 10 \text{ cm}\) is made of a material with a shear modulus of \(G = 101,80 \text{ GPa}\). Calculate the moment of inertia for the torsion of the cross-section: \(J_s\) in \([\text{cm}^4]\). For a doubly supported rod, loaded along its entire length with a uniformly distributed moment of intensity \(10 \text{ kNm/m}\) and a concentrated moment in the cross-section \(B\) with a value of \(M_0 = 30 \text{ kNm}\), acting opposite to the distributed moment, draw the graphs: \(M_s\) - torsional moments - section forces and describe in \([\text{kNm}]\). \(\varphi\) - angles of rotation relative to the support and describe in \([10^{-3} \text{ rad}]\). Note: describe the extrema - that is, indicate on the drawing where they will occur and what their values will be. Calculate the maximum value of shear stress in this rod: \(\tau_{\text{max}}\) \([\text{MPa}]\).

Determine the elastic load-bearing capacity \( M = M_s \) and the limit \( M = M_n \) of the given twisted rod below. Determine the ratio \( M_n / M_s \). For the determined values \( M_s \) and \( M_n \), create graphs of the twisting moments. In the calculations, assume \( G = 26 \, \text{GPa} \), the Tresca hypothesis, and the above-given values \( a \) and \( R_{pl} \) (under tension).