the spar platform shown above has a circular cross section with
diameter D (upper part) and 2D (lower part). It is floating in a
very deep water.
a. Derive an expression for the natural frequency.
Given, a platform is floating on water for which we need to determine the natural frequency which is stated as simple harmonic equation.
We are going to use newton's second law and buoyancy forces to find SHM.
From the obtained simple harmonic motion equation we find the natural frequency.
The above discussed is represented in the below image:
the spar platform shown above has a circular cross section with diameter D (upper part) and 2D (lower part). It is float...
Stress Transformation: 16a The shaft has a circular cross section of diameter d 35 mm, and is subjected to torque T 24 Nm in the direction shown. Consider a material element positioned on the outer surface of the cylinder and oriented at 450 as shown. Find the magnitude of the stresses on that element and draw them (with the correct direction) in a properly oriented element. 45
A Solid ac bar has a circular cross section of 30 mm diameter.
For the shown torques, Calculate the angle of twist Φac of the
entire shaft, knowing that G = 70 GPa.
T 10 kN·m 4 m 3 m
1. The part shown consists of a bent rod with a solid circular cross section of diameter 20 mm. Consider the cross- section on a cut at both a-a, and b-b. 400 mm A] For each cut, label the shear force, bending moments, and torsion moments. Then determine the critical point with the highest normal stress at each cross- section. No stress calculations are required. /100 mm 1 BJ Determine the point of highest normal stress for the bent rod...
1. A steel bar with solid circular cross section has a diameter d= 2.5 in., a length L = 60 in. and a shear modulus of elasticity G = 1 1.5 × 106 psi. The bar is subjected to torque T- 350 lb-ft as shown. (a) Find the angle of twist between the d 2.5 in (b) Find the maximum shear stress in the (c) Find the shear stress ta at a distance (d) Find the shear stress Tcenter at...
Bar A bar of a circular cross section of a diameter d = 8.2 mm has a length of L = 5.4 m is fixed at one end and free at the other. A force P = 7.9 kN is applied at the free end of this bar. Determine the stiffness of the bar. Assume E = 200 GPa Give your answer in units of N/mm Select one Oa. 1165.93 Ob 1955.93 c. 62.44 Od. 15451.85
The part shown in the figure has a circular cross-section of
0.04 m diameter. It is made of a steel with a yield strength of 343
MPa and an ultimate strength of 410 MPa, and is subjected to a
force, F, of 2500 N.
1. Locate the most critical point. (2 points)
2. Plot the three-dimensional stress element for that point. (2
points)
3. Calculate the values of stresses. (6 points)
Fぐ
Fぐ
3. A beam with a hollow circular cross section of outer diameter D and inner diameter d. The length Lis fixed at a wall. Consider the following loading conditions, all applied to the beam at the midpoint of length L. For each loading scheme state determine the magnitude of that stress in terms of the variables given in the problem). (5 points) i. ii. iii. iv. V. Normal stress due to axial load F Shear stress due to torque T...
The truss is made from A992 steel bars, each of which has a circular cross section with a diameter of 2.1 in (Figure 1) Part A Determine the maximum force P that can be applied without causing any of the members to buckle. The members are pin connected at their ends. Express your answer to three significant figures and include the appropriate units.
A solid steel bar of circular cross section has diameter d = 40 mm, length L = 1.3 m and shear modulus of elasticity G = 80 GPa. The bar is subjected to torques T acting at the ends. If the torques have magnitude T = 340 Nm, what is the maximum shear stress in the bar? What is the angle of twist between the ends? If the allowable shear stress is 42 MPa and the allowable angle of twist...
A steel tube with a circular cross section has an outside diameter of 300 mm and wall thickness of 2 mm. The cylinder is twisted along its length of 2 m with a torque of 50 kN · m. (a) Determine the maximum torsional shear stress using Equation Theta= T*L/JG (b) Determine the maximum torsional shear stress using the closed thin-walled tube method. Compare this result to the result of part (a). (c) Assuming the tube does not yield, determine...