A cantilever beam with a uniform flexural rigidity (EI=200 * 10^6 N.m2) is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the beam is 10000 N.m2 .Find the magnitude of the slope of the beam at its free end in micro radian?
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- Answer the following items. Calculate the shear force and bending moment for the beam subjected to the loads, then draw the shear force diagram and bending moment diagram. 1. A simple beam 10 meter long carries a concentrated load of 20OKN at the midspan. 2. A simply supported beam, 10m long carries a uniformly distributed load of 20 KN/m. 3. Cantilever beam 10 meter long carrying a distributed load with intensity varying from 20KN/m at the free end to zero at the wall. 30 kN/m В *1m: RD 3 m 2 m 4. RA 10 kN/m 12 kN 3 kNm 2 m 4 m 1 m 5.The bending moment diagram and cross-section for a beam are shown below. Use the elastic flexural formula ox = -Mzy/l, to determine the required strength of the beam to resist the compressive stresses. Circle the correct answer for the compressive strength in ksi: 2.3, 2.5, 27.5, 30, 37.7 Show your work below. Bending Moment Diagram Beam Cross-Section 4" +50 2' (K-Fe) 2" 2" - 40 2"Consider an 8-m long simply supported T-beam with overhangs loaded as shown below. 200 mm w kN/m 50 mm 50 kN-m 50 kN-m 200 mm 2 m 4 m 2 m 50 mm 1. Determine the location of the neutral axis measured from the top of the beam and the moment of inertia (in mm4) of the section about its neutral axis. Draw the shear and bending moment diagrams. Annotate all relevant values and distances. Determine the magnitude of the maximum negative 2. moment. Determine the minimum allowable strength of the beam in tension and the minimum allowable strength of the beam in compression. 3. Determine the maximum allowable load, w (in kN/m), that can be applied pn the beam. 4. B.
- A beam is supported and loaded as shown. In the section of the beam between 'A' and 'B', the equation for the resisting bending moment was determined as: Mr = -6.2x²+50x. Determine the magnitude of maximum resisting bending moment (Mcmax) in the section. Note: Do NOT include units in your answer Answer: AY FunFor 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 cmA simply supported beam is shown. The maximum bending moment is at B. Use the method of sections to determine the moment at B. Then determine the required section modulus needed for an allowable bending stress of 24 ksi. Verify that two L4x3 angles placed as shown will support the loading based on the angle thickness you select using Appendic C. Ans: Ms = 4350 Ib-ft %3D 2000 Ib 300 lb/ft 6 in, CTI 4 in. 3 ft 3 ft
- A beam is supported and loaded as shown. In the section of the beam between 'A' and 'B', the equation for the resisting bending moment was determined as: M₁ = -6.5x²+50x. Determine the magnitude of maximum resisting bending moment (Mr,max) in the section. Note: Do NOT include units in your answer Answer: AA BGiven the beam shown below (E=200GPa, I=180x106 mm4, 80mmx300mm), do the following: a. Draw the shear force and bending moment diagrams b. Find the magnitude and location of the maximum tensile bending stress c. Using superposition, find the elastic curve and then the deflection of the beam at B, C, and D 8kN 4kN A B 4m 3m 3mFor 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 X
- Give the following problem a try. If you get stuck, here is one way to work it: Essential Solution Video. Determine the bending moment M in the beam at the point located L = 3.15 m to the left of point C. The ground reactions and shear- force diagram are shown. 40.0 KN Units: KN 3 m B 65.60 KN 65.60 65.60 25,60 O 202.5 kN-m O 163.5 kN-m O 149.2 kN-m O 120.1 kN-m O 110.0 kN-m 7.0 kN/m 12 m @x=6.66 m 58.40 KN -58.40 XA 8-kN load is supported by a cart that rolls along a beam as shown in Fig. Plot Mmax, the maximum bending moment in the beam, as a function of the cart's position b (1s bs 6 m). 8 m 200 mm 200 mm B D 8 kNFor 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