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- Find expressions for shear force V and moment Mat x = 2L/3 of beam (a) in terms of peak load intensity q0and beam length variable L. Repeat for beam (b) but at x = L/2.Find expressions for shear force V and moment M at mid-span of beam AB in terms of peak load intensity q0and beam length variables a and L Let a = 5L/b.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.
- For the overhang beam shown below, (a) draw the free body diagram of the beam, (b) draw the shear and moment diagrams, (c) find moment of inertia of its cross-section, (d) determine the maximum bending stress. (e) indicate the stress components on an infinitesimal volume element (3D stress element) located at the point. Neglect the weight of the beam. 8 kN/m 2 cm em A C 25 em B 4 m 2 m 2 cm 20 cm4. The box beam is made of an elastic-perfectly plastic material for which the yield 250 MPa. Draw the residual stress distribution in the beam after the elastic-plastic moment, Mep = 548.5 kNm, is applied and then released. It can be shown that under the applied moment, the flanges (260 mm × 30 mm) yield, while the webs (2 x 200mm x 30mm) show linear elastic behavior. The moment of inertia and plastic section modulus of the section are given below: I = 247.48 x 106 mm4; Z, = 2394000 mm³ stress oy = y 30 mm 30 mm 200 mm 200 mm 30 mm 30 mmA 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 is
- For the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.50 m, b=4.25 m, PB = 45kN, and Pc = 90kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = Dy= Mi i B Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) PB a PB B a Pc a Pc C kN b KN b D X D₂ XThe Cantilever beam in Fig. 5, has a circular cross section (diameter-100 mm) (a)find the shear stress in the beam in points (a,b.c.d and e) due to applied the uniform load 3 kN/m and the torque 4kN.m. (2) Sketch the shear stress distribution over the cross section. Dia 100 mm B. 3 kN/m 4 kN.m C. 4 m 1 m FigFor the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.75 m, b=5.00 m, PB = 60KN, and Pc = 80kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = Dy= tel tel a i B a Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) PB B a PB Pc a C Pc C KN b KN D b D X D₂ X
- 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 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 4For the beam shown, the magnitude of the concentrated load is P = 21 kN, the magnitude of the couple is MB = 210 kN-m, and the beam lengths are a = 4.3 m and b = 12.9 m. (a) derive equations for the shear force V and the bending moment M for any location in the beam. Place the origin at point A. (b) use the derived functions to plot the shear-force and bending-moment diagrams for the beam. Use your diagrams to determine the magnitudes of the maximum shear force and the maximum bending moment. Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number. MB b a Answer: kN max kN-m Mmax i %3D B.For a beam subjected to the load F at the center of the span as shown below, please 1. Find the maximum allowed load F, given a. Modulus of Rupture (MOR) of the material for the beam = 130 GPa b. Beam width b = 0.02m and depth d = 0.05m c. Span length L = 10m 2. If the maximum allowed load F is designed to be 40,000N, given all other conditions the same, what is the minimum MOR required for the material to make the beam? 3. If the maximum allowed load F is designed to be 50,000N, given all other conditions (MOR = 130 GPa) the same, what is the minimum depth d required? F b ✰ d ↓ D L