g) h) 5 KN 50 mm 20 mm 150 mm 40 mm 2 kN 200 mm...

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g) h) 5 KN 50 mm 20 mm 150 mm 40 mm 2 kN 200 mm 5 kN 1 kN Three forces are applied to member ABD as shown. The cross-section is a hollow rectangle with 20mm height and 40mm width and a wall thickness of 2mm. and K are located at half the width and half the height of the member on its surface and in the same cross-section. To determine the principal stresses and their orientation in points Hand K: (HINT: The parts between the dashed lines can be solved independently using the intermediate results given.) a) Draw a free body diagram of the part HBD of the member b) Introduce the proper internal reactions c) Using the given coordinate system and equations of equilibrium show, that these are N = -5kN; Vy=-3kN;V₂ = -5kN; M. = 200Nm; My = 750Nm; M₂=-450Nm; d) Show the part AH of the member along with the (now know) internal reactions e) Sketch the stress distributions of each individual load (torsion, bending etc.) in the whole cross-section resulting from POSITIVE internal reactions. f) Determine the stresses in points H and K. Use your sketch from e) along with the positive coordinate directions to determine the correct components and signs of the stresses Calculate (no Mohr's circle!) the principal stresses along with their orientation in points H and K Draw a figure showing these principal stresses with their orientation at points H and K on the beam. i) Sketch the projected beam looking at the x-y plane such that the z-axis is pointing at you. Forces being behind each other are added, forces acting in or against the z-direction drop out. j) Determine the support reactions - compare to the results of c) k) Draw the shear force and bending moment diagram 1) Express the bending moment as a function of x m) Get the deflection at B by integrating the deflection curve starting with the second order differential equation based on M(x) n) What is the angle of deflection in the x-y plane from this result? o) What is the angle of twist due to torsion in point B? p) Bonus: Can you get the deflection at D from the results of m)-o)? What is it? HINT: The parts between the dashed lines can be solved independently using the intermediate results given. g) h) 5 KN 50 mm 20 mm 150 mm 40 mm 2 kN 200 mm 5 kN 1 kN Three forces are applied to member ABD as shown. The cross-section is a hollow rectangle with 20mm height and 40mm width and a wall thickness of 2mm. and K are located at half the width and half the height of the member on its surface and in the same cross-section. To determine the principal stresses and their orientation in points Hand K: (HINT: The parts between the dashed lines can be solved independently using the intermediate results given.) a) Draw a free body diagram of the part HBD of the member b) Introduce the proper internal reactions c) Using the given coordinate system and equations of equilibrium show, that these are N = -5kN; Vy=-3kN;V₂ = -5kN; M. = 200Nm; My = 750Nm; M₂=-450Nm; d) Show the part AH of the member along with the (now know) internal reactions e) Sketch the stress distributions of each individual load (torsion, bending etc.) in the whole cross-section resulting from POSITIVE internal reactions. f) Determine the stresses in points H and K. Use your sketch from e) along with the positive coordinate directions to determine the correct components and signs of the stresses Calculate (no Mohr's circle!) the principal stresses along with their orientation in points H and K Draw a figure showing these principal stresses with their orientation at points H and K on the beam. i) Sketch the projected beam looking at the x-y plane such that the z-axis is pointing at you. Forces being behind each other are added, forces acting in or against the z-direction drop out. j) Determine the support reactions - compare to the results of c) k) Draw the shear force and bending moment diagram 1) Express the bending moment as a function of x m) Get the deflection at B by integrating the deflection curve starting with the second order differential equation based on M(x) n) What is the angle of deflection in the x-y plane from this result? o) What is the angle of twist due to torsion in point B? p) Bonus: Can you get the deflection at D from the results of m)-o)? What is it? HINT: The parts between the dashed lines can be solved independently using the intermediate results given.

Answer rating: 100% (QA)

Introduce the proper internal reactions Using the given coordinate system and equations of equilibrium show that these are N5kN Vt3kNt V25kN M0200Nm M175 M450Nm Show the part AH of the member along wi... View the full answer