(a) Determine the internal loadings, including axial force, shear force, and bending moment at point C in beam AB. AFI 4m 5kN/m O C B Du 1m 1m 2m
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- The cross section of a sand wie h beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in, the thickness I of the faces is 0.25 in., and the height hcof the core is 5.5 in. (total height h = 6.0 in). The moduli of elasticity are 10.5 × 106 psi for the aluminum faces and 12.000 psi for the foam core. A bending moment M = 40 kip-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.A sandwich beam having steel faces enclosing a plastic core is subjected to a bending moment M = 5 kN · m. The thickness of each steel face is 1 = 3 mm with modulus of elasticity E = 200 GPa, The height of the plastic core is hp= 140 mm, and its modulus of elasticity is Ep= 800 MPa. The overall dimensions of the beam are h = 146 mm and h = 175 mm. Using the transformed-section method, determine the maximum tensile and compressive stresses in the faces and the core.Consider a 6−m6−m long horizontal beam supported by a pin at one end and a roller at the other end. If a 30kN⋅m30kN⋅m bending moment is applied at the roller end of the beam, what is the internal bending moment at a distance of 2m2m from the pin?
- Consider the beam section below where fc’ = 30 MPa, Es = 200 GPa, determine the bending stress of the steel section if M=180 KN-m in MPa. Express your final answer in two decimal places.A beam of rectangular section of 12 cm × 20 cm is simply supported over a span of 12 m. It is acted upon by a load of 80 kN at the mid span. Determine the maximum bending stress induced in thr beam.N for Newton, m for meter, mm for millimeter, N/(mm^2) for Stress, mm^2 or m^2 for Area, mm^4 for Moment of inertia and Nm for bending moment. Use brackets if the power is MINUS for Example: 0.00125 N =1.25*10^(-3)N. 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 Solution: (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
- Consider the beam shown. Suppose that w1 = 600 N/m , w2 = 300 N/m . Follow the sign convention. A) Determine the internal normal force at point C. NC = ? B) Determine the internal shear force at point C. VC = ? C) Determine the internal moment at point C. MC = ?The beam safely supports shear forces and bending moments of 2kN and 6.5 kN-m respectively. Based on this criterion, can it be safely subjected to the loads F = 1kN and C = 1.6 kN-m?A horizontal beam under bending has a maximum bending stress of 100 MpA and a maximum shear stress of 20 Mpa. What is the maximum principal stress induced in the beam.
- A simply supported beam AB = 11 m has a hollow rectangular cross-section with 11 cm as width, 28 cm as depth and inner thickness as 1 cm is subjected to a point load of 5 N & 6 N acting at C and D respectively and a uniformly distributed load (UDL) of 9 N/m starts from mid-span and ends at the right support of the beam. Determine the maximum bending stress and the bending stress at 1 cm from the top. Take AC = 1 m & CD = 1 m. iv) Maximum Bending Moment (Please write the Maximum bending moment valve in "Nm") = v) Moment of Inertia, I = vi) Maximum bending stress = vii) Bending stress at 1 cm from the top =A simply supported beam AB = 9 m has a hollow rectangular cross-section with 13 cm as width, 20 cm as depth and inner thickness as 1 cm is subjected to a point load of 8 N & 8 N acting at C and D respectively and a uniformly distributed load (UDL) of 9 N/m starts from mid-span and ends at the right support of the beam. Determine the maximum bending stress and the bending stress at 1 cm from the top. Take AC = 1 m & CD = 2 m. i) Reaction force at B in (N)= ii) Reaction Force at A in(N)= iii) The distance from B at which the shear Force value changes from "-" to "+" in (m)= iv) Maximum Bending Moment (Please write the Maximum bending moment valve in "Nm") = v) Moment of Inertia, I in (m^4)= vi) Maximum bending stress in (N/m^2)= vii) Bending stress at 1 cm from the top in (N/m^2) =N for Newton, m for meter, mm for millimeter, N/(mm^2) for Stress, mm^2 or m^2 for Area, mm^4 for Moment of inertia and Nm for bending moment. Use brackets if the power is MINUS for Example: 0.00125 N =1.25*10^(-3)N. A simply supported beam AB = 11 m has a hollow rectangular cross-section with 14 cm as width, 29 cm as depth and inner thickness as 1 cm is subjected to a point load of 6 N & 8 N acting at C and D respectively and a uniformly distributed load (UDL) of 8 N/m starts from mid-span and ends at the right support of the beam. Determine the maximum bending stress and the bending stress at 1 cm from the top. Take AC = 1 m & CD = 2 m. Solution: i) Reaction force at B = ii) Reaction Force at A = iii) The distance from B at which the shear Force value changes from "-" to "+" = iv) Maximum Bending Moment (Please write the Maximum bending moment valve in "Nm") = v) Moment of Inertia, I = vi) Maximum bending stress = vii) Bending stress at 1 cm from…