# Discussion on advance mechanics of materials

need help for HW
hello Y’ll,I am taking advance mechanics of materials and I need help solving this Homework. the Homework file uploaded below.

HW7: CE-4440 Advanced Strength and Applied
Elasticity
Fall 2020
Due, Tues. Dec. 1st
S.Moorthy, 3255F PFT
Phone: 578-4846,Email:[email protected]
1) If the torsional solution for a cylinder of equilateral triangular cross-section shown in figure, is
to be determined using the Prandtl stress function Φ = k(x−√3y− 2 3h)(x+√3y− 2 3h)(x+ 1 3h),
(a) Verify that the stress function Φ satisfies Poisson′s equation
(b) Calculate the shear stress τzx(x, y) and τzy(x, y) for given torque T acting on the cross-section
of the beam
(c) Calculate the angle of twist per unit length θ for given torque T and calculate the effective
polar moment of inertia Je of the cross-section
(d) Calculate the warping function w(x, y) for the cross-section (Grad students only)
.
.
3
3
3

h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). . h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). . h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). . h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). . h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). . h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). . h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). . h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). . h/ 2h −−−−− h −−−− 3 3 h 2h x=− y+−−−− 2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in figure. Calculate the shear stress distribution and the angle of twist per unit length for each cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last cross-section). .

h/
2h
−−−−−
h
−−−−
3
3
h
2h
x=− y+−−−−
2) An internal torque T = 2.5 mN · m acts on each of the three thin cross-sections shown in
figure. Calculate the shear stress distribution and the angle of twist per unit length for each
cross-section. (Assume G = 40 GPa and t1 = t2 = t4 = 2 mm and t3 = t5 = 3 mm for the last
cross-section).
.

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