A beam with rectangular cross section has b = 50 mm, h =150 mm, E = 210 GPa, and o, = 250 MPa. Find the yield moment My, the plastic moment Mp, and the shape factor f. %3D y M h b
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- A singly symmetric beam with a T-section (see figure) has cross-sectional dimensions b = 140 mm, a = 190, 8 mm, b. = 6,99 mm, and fc = 11,2 mm. Calculate the plastic modulus Z and the shape factor.A steel beam of rectangular cross section is 40 mm wide and 80 mm high (see figure). The yield stress of the steel is 210 MPa, (a) What percent of the cross-sectional area is occupied by the clastic core if the beam is subjected to a bending moment of 12.0 kN · m acting about the z axis? (b) What is the magnitude of the bending moment that will cause 50% of the cross section to yield?The hollow box beam shown in the figure is subjected to a bending moment M of such magnitude that the flanges yield but the webs remain linearly elastic. (a) Calculate the magnitude of the moment M if the dimensions of the cross section are A = 15 in., A] = 12.75 in., h = 9 in., and ey =7.5 in. Also, the yield stress is eY = 33 ksi. (b) What percent of the moment M is produced by the elastic core?
- A wood beam 8 in. wide and 12 in. deep (nominal dimensions) is reinforced on top and bottom by 0,25-in.-thick steel plates (see figure part a), (a) Find the allowable bending moment A/max about the z axis if the allowable stress in the wood is 1100 psi and in the steel is 15,000 psi, (Assume that the ratio of the moduli of elasticity of steel and wood is 20.) (b) Compare the moment capacity of the beam in part a with that shown in the figure part b which has two 4 in. × 12 in, joists (nominal dimensions) attached to a 1/4 in, × 11.0 in, steel plate.A wood beam with cross-sectional dimensions 200 mm x 300 mm is reinforced on its sides by steel plates 12 mm thick (see figure). The moduli of elasticity for the steel and wood are E±= 190 GPa and Ew= 11 GPa, respectively. Also, the corresponding allowable stresses are eS= 110 MPa and ew = 7.5 MPa, (a) Calculate the maximum permissible bending moment Mmaxwhen the beam is bent about the- axis. Repeat part (a) if the beam is now bent about its y axis. Find the required thickness of the steel plates on the beam bent about the y axis so that Mmaxis the same for both beam orientations.A bending moment due to load applied on the head of femur bone which is offset by a distance (x= 50 mm) off the bone center for a person standing in relaxation.His weight is 70kg.1. Find the maximum bending stress induced due to the weight and compare it to the maximum comp. stress. R= 20mm t= 12mm.2. Draw the expression for the second moment (I) basing on min-wall hollow cylinder.3. Find the principal stress σ1, σ2, τx1y1, and the angle θp for point C and D shown.
- The shape of the beam made of U profile ensures safe loading. Find the length c of the overhangs so that it can move. Of the material Safety stress (ç) emn = 50 N / mm2 for tension and compression conditions, (ob) emn = 80 N / mm2. Support spacing of the beam L = 6 m, cross section its dimensions are a = %D 210 mm, b = 150 mm and wall thickness t = 40 mm. The loading condition is P = 30 kN and qo = 40 kN / m. P B (Kesit)A beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3.6 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 0.5 cm from the neutral axis (i) The moment of inertia = ii) The radius of curvature is (iii) The maximum bending stress is iv) The bending stress at the point 0.5 cm from the neutral axis isA beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3.7 cm and internal diameter 2.2 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 (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 Answer and unit for part 4
- Consider the beam shown. Suppose that M= 9 kip*ft, P=8 Kip,w=1.4 kip/ft and point D is located just to the left of the 8-kip load. Follow Sign Convention. Find the Internal force at section passing through point D for Np ,VD, Mp, VẸ, MẸ M E C A 6 ft 6 ft 4 ft 4 ftA 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 4Problem 4 For the beam shown below, find the value of EIY at 2m from R2. E= 18500MPa and; beam cross -section=200mmX275mm . Use Area-moment method w=15kN/m