torsion3b - Then T= Example 4mm A stell bar G=200GPa of...

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04.01.10 Taner YILDIZ Coşkun TUNCA AE 361 APPLIED ELASTICITY LECTURE NOTES Prandtl Stress Function …………(*) 6.5 Prandtl’s Membrane Analogy Equation (*) is the same form as the equation describing the deflection of a membrane (or soap film) subject to pressure. ( ) Derivation: Equation for the deflection z Let the tensile force per unit membrane length be denoted by s = constant.
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, Comparison
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TORSION OF THIN WALLED MEMBERS with OPEN CROSS SECTION
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Boundary conditions: at at Volume of the parabolic cylindircal membrane is V= = Define an effective polar moment of inertia = b for rectangular cross section T=2V= b Gθ= λ max SHEAR STRESS λzy= - =2Gθx Angle of Twist per unit length λ max= Gθt θ=
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Unformatted text preview: Then T= Example 4mm A stell bar G=200GPa of croos section shown is subject to a torque of 500 Nm Determine max shear stress? Solution J e= J e1+ J e2 = 1/3b 1 t 1 3 +1/3b 2 t 2 3 = 1/3*(100)*(10) 3 +1/3(125)*(4) 3 = 3,5787*10 4 mm 4 λmax= where t=t 1 = 500*(0,01)/3,578*10 4= 139,7 MPa θ= = 69,86*10-3 rad 10mm 100mm 125mm For this rectangular section force equation equals , Fz=0 λ 1 dzt 1 + λ 2 dzt 2 =0 λ 1 t 1= λ 2 t 2= q=shear flow and it is constant Area= the net force on the element is λ (ds.t)=qds the total torque T t 0 to (rcos )qds T=q 2dA T=2qA & λ = z Angle of Twist γL= θ r for ds element γL = θdsrcos = Θds=G Angle of Twist= θ = Θ= Θ= Θ= J e=...
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