25 K 15 K 6ft 4 ft 3.0 K/ft 4 Use the free-body diagram pproach shown in Sections 5-3troush 5-5 o deermine the iemal shearing krce and bending moment at any specified point in a beam. 5. Write equations for all seganents of the shearing force and bending moncat diagrams wsing the guidelines pre- sented in Section 5-10.
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- Problems 5-117 through 5-122 Figures P5-117 through P5–122 show completed bending moment diagrams for beams. Develop the shearing force dia- gram and the loading diagram for each beamIn Figure Q5b, a beam is supported at A and C with a uniformly distributed load (UDL) of 38.75 kN/m between A and B. Distance L1 = 9.00 m and L2 = 4.50 m. Draw and label the shear force diagram (SFD) and bending moment diagram (BMD) for the beam shown in Figure Q5b. Label the shear force and the bending moment values at points A, B & C on both diagrams; determine the distance from A along the beam where the shear force is zero; and calculate the bending moment at the point where the shear force is zero. Clearly indicate the type of bending between AC and between BC. A UDL L1 Figure Q5b B L2 CIn Figure 4a, a beam is supported at A and C with a uniformly distributed load of 20 kN/m between A and B. Draw and label the shear force diagram (SFD) and bending moment diagram (BMD) for the beam shown in Figure Q3a. Label the values for shear force and bending moment at points A, B, C & at the beam mid-point M; the maximum bending moment and its distance from A; and clearly indicate the type of bending between AB and between BC. (show all work)
- For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a-3.25 m, b=4.75 m, Pg - 35kN, 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. A Ay- 58.66 - Dy- Calculate the reaction forces A, 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.) Answers: a 56.33 (a) V= (b) V- (c) V- B i i PB B kN с kN C Determine the shear force acting at each of the following locations: (a) x-2m (b)x - 4 m (c) x-8 m Note that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2. 3 3 3 KN D b kN D ·x Dy2. Draw shear force and bending moment diagrams for the beam shown in figure. 50 kN/m 20 kN/m D to 2 m 2 m 2 m RA Ro 3. Relation between load, shear and moment: Please solve according to the exporters of a typícal solution. We will discuss the relations existing between the loads, shears and bendin moments in any beam. Theses relations provide a method of constructing she and moment diagrams without writing shear and moment equations. The beam shown in figure (1) is assumed to carry any general loading. The free body diagram jar - jute W Nm) of segment of this beam of length (dx) is shown in figure (2). wtx = is the summation of area between (x) and x;) but V, -V, = AV = (area) similarly (1) (2) EF, -0>V+ wdx-(V+dV)=0 -Intensity of load (N/m) . dV = wdx EM, 0= M+Vdx + (wcbx) - (M + dM) =0 dM = M, - M, - AM = (area ) AP dx (de) ~zero 2 . dM=Vde Where: (slope of shear diagram) .V = INP (slope of moment diagram) for (dV = wdx) we can integrating deHomework -3- Q1: A simply supported beam as shown in figure (1-A) below, having an I-cross section, has an over all width 200 mm and all depth 300 mm with flanges and web of thickness 20 mm shown in figure (1-B). (a) Draw the shear force and bending moment diagrams of the beam; (b) Determine the maximum compression and tension bending stress which can setup in the beam. 25 20 kN 20 kN 10 kN 150 60 kN/m (All dimensions in mm) 30 kN/m 100 1.5 m Im Im Im 50 50 50 50 50 Figure (1-A) Figure (1-B) Q2: A simply supported beam AB has a length of 3 m and carries distributed load which varies in linear manner from (1w) N/m at A support to (2w) N/m at the B support and concentrated load (1.5w) N at 2 m from A support, and the beam has hollow circular cross section of diameter ratio dindout =1/3. Draw S.F. and B.M. diagrams for the beam and determine the value of (w) if the maximum bending stress 110 N/mm?, and the average shear stress at 1 m from point A equal to 15 N/mm?.
- Draw and label the diagram correctlyShow the complete solution. Determine the following:a. Shear and Bending Moment Equationb. Shear and Bending Moment Diagramc. MmaxFor the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a-3.25 m, b=4.75 m, Pg = 35kN, 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 = a M. B a PB 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 Pc a Pc kN b KN D b D X D XThe shaft in the diagram below is s supported in bearings near its ends at A and D and is subjected to the following: Reaction force at 'A' of 14,000N, Reaction force at 'D' of 13,000N Bending forces of 18,000N at 'B' and 9,000N at 'C' as shown in the diagram. Calculate the maximum bending moment in the shaft.. Give your answer to 1 d.p. in Nm but do not include units in your answer. e.g. 5000.0 NOT 5000Nm 300mm B 400mm 200mm C A D
- In Figure Q3a, a beam is supported at A and C with a uniformly distributed load of20 kN/m between A and B. Draw and label the shear force diagram (SFD) andbending moment diagram (BMD) for the beam shown in Figure Q3a. Label thevalues for shear force and bending moment at points A, B, C & at the beam midpoint M; the maximum bending moment and its distance from A; and clearlyindicate the type of bending between AB and between BCThe figure shows a cantilevered beam, subjected to a uniformly distributed (rectangular) 40 N/m force along the section DE, a 50 N point force at point C, and a 200 Nm couple moment. a. Write the shear-force and bending-moment equations as a function of distance, x, measured from the leftmost point, A, for the entire beam. b. Using your shear-force and bending-moment equations, calculate the shear force and bending moment at x = 2 m and x = 5 m. 200 N·m A 2.5 m 50 N CV D 1 m 40 N/m ↓↓↓ 2.5 m E B 2 mQ/ For the beams and loading shown below. A-Draw the shear force and bending-moment diagrams. B- Determine the equations of the shear force and bending-moment curves for the segments CD in Figure 2 C- Compute the bending stress at point (a) on section C. D- Determine the values and locations of the maximum tensile and compression bending stresses. Figure (2) R Point a Radius of hole: 40kN 0.5m 30 20KN/m 0.7m A B D |B 1m Im 3m Radius = R= 100 mm