Before obtaining the slope and deflection at any point on the elastic curve, why is it necessary to relate the internal moment to the radius of curvature?
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Before obtaining the slope and deflection at any point on the elastic curve, why is it necessary to relate the internal moment to the radius of curvature?
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- For the wire form shown, use Castigliano's method to determine the deflec- tion of point A in the y direction. Consider the effects of bending and torsion only. Use the straight beam formulation for the bending energy. The wire is steel with E 200 GPa, v = 0.29, and has a diameter of 5 mm. Before cation of the 200-N force the wire form is in the xz plane 100 mm. = appli- where the radius R isFor the simply supported beam carrying the concentrated load P = 268 N at its midspan, determine the magnitude of the maximum displacement (in mm) if d = 1.51 m, E = 11.77 GPa , and I =1679930mm4. NOTE: PLEASE ANSWER IT CORRECTLY. IF YOU ARE NOT SURE ABOUT THE ANSWER, PLEASE SKIP THE QUESTIONPLEASE BOX THE FINAL ANSWER(S)THANK YOU! image below for referencebeam, simply supported at its ends, carries a load which increases uniformly from 15kN/m at the left-hand end to 100 kN/m at the right-hand end. If the beam is 5m long, find the equation for the rate of loading and, using this, to determine the deflection of the beam at mid-span if E= 200GN/m² and I=600*10 m².
- Problem 4 The overhanging steel beam ABC carries a concentrated load P at end C. For portion AB of the beam, (a) derive the equation of the elastic curve, (b) determine the maximum deflection, (c) evaluate vmax for the following data: W14 × 68 | = 722 in4 E = 29 x 106 psi P = 50 kips L = 15 ft = 180 in. %3D a = 4 ft = 48 in %3D х- -by- Flange Web Thick- Thick- Axis X-X Axis Y-Y Depth d, in. Area Width ness ness Designation' A, in? br, in. to, in. L in. in S, in F in. in' S, in in. W14 x 370 109 17.9 16.5 2.66 1.66 5440 607 7.07 1990 241 4.27 145 42.7 14.8 15.5 1.09 0.680 1710 232 6.33 677 87.3 3.98 82 24.0 14.3 10.1 0.855 0.510 881 123 6.05 148 29.3 2.48 68 20.0 14.0 10.0 0.720 0.415 722 103 6.01 121 24.2 2.46 53 15.6 13.9 8.06 0.660 0.370 541 77.8 5.89 57.7 14.3 1.92 43 12.6 13.7 8.00 0.530 0.305 428 62.6 5.82 45.2 11.3 1.89 6.77 0.515 0.310 385 54.6 5.87 26.7 7.88 1.55 38 11.2 14.1 *You can draw a FBD, Shear V-diagram, and a Bending Moment-M diagram to help in determining the shear…Consider the beam with properties and loadings as described in the figure and parameter table. Determine the equations for the deflection in mm: One on the interval 0 ≤ x < aL and the other on the interval aL ≤ x ≤ L. -aL- mm parameter E Beam Type L a P P value for 0 ≤ x < aL: v₁(x) = 209 W360 x 64 2.7 0.4 for aL ≤ x ≤ L: v₂(x) = (cc) + 2022 Cathy Zupke 8 BY NO SA -(1-a)L- units GPa m [-] KN B Enter an algebraic expression [more..]A beam has a bending moment of 3 kN-m applied to a section with a hollow circular cross-section of external diameter 3.4 cm and internal diameter 2.4 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solve the number four (iv) only ; (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is iv) The bending stress at the point 0.6 cm from the neutral axis is in (N/mm^2)
- A beam has a bending moment of 2.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3 cm and internal diameter 2.3 cm. The modulus of elasticity for the material is 210 x 10° N/m². Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.7 cm from the neutral axis Solution: (i) The moment of inertia = %3D ii) The radius of curvature is (iii) The maximum bending stress is iv) The bending stress at the point 0.7 cm from the neutral axis is70 mm Mx G 165 mm Mx = 79ヒNm %3D 60 mm 190m Mx affects the cross section digure. Calculate the noral stress values The bending moment of the beam given in n that will occur at the points I,2, 3 of the beam sectio and draw the noral stress distribution.A beam has a bending moment of 4.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3.1 cm and internal diameter 2.1 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solution: - The bending stress at the point 0.6 cm from the neutral axis is
- A beam has a bending moment of 2.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3 cm and internal diameter 2.3 cm. The modulus of elasticity for the material is 210 x 109 N/m. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.7 cm from the neutral axis Solution: (i) The moment of inertia = 26024.12mm^4 ii) The radius of curvature is 2186.02mm (iii) The maximum bending stress is 1.44GPA iv) The bending stress at the point 0.7 cm from the neutral axis isA beam has a bending moment of 3 kN-m applied to a section with a hollow circular cross-section of external diameter 3.4 cm and internal diameter 2.4 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis Solution: (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is in (N/mm^2) Answer and unit for part 3 iv) The bending stress at the point 0.6 cm from the neutral axis is in(N/mm^2) Answer and unit for part 4In the beam, which is given the loading and supporting status below a) Find the location of the largest crash and the value of the crash. b) What is the maximum length of the beam (L) so that the largest collapse value is less than 1.5 mm? E = 210 GPa Mo = 250 kNm I = 556x10-6 m4