a) Determine the reactions at supports B (pin) and C (roller). b) Determine the internal loading at x= 10 m (point E) measured from point A. Write functions for shear force (V) in terms of x
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- Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a = 5 m, b = 3 m, PB = 55 kN, Pc = 75 kN, and PE = 25 kN. 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 PB Answer: Ay = i BO PB a B Pc 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.) D Pc D a D₂ PE a PE E kN, Dy= i -x E X kN.3 For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment diagrams. V = 9 kN, V2 = 9 kN, V3 = 200 mm, and V4 = 1100 mm. ATAT-V3 Provide values at all key points shown in the given shear-force and bending-moment diagrams. X (mm) B A = B = C = D = E= F= P = Q = E * KN * KN * KN × KN KN x KN ✩ kN.mm *kN.mm D 0.00 Reaction force R₁ (left) = In the shear-force and bending-moment diagrams given, +V 0.00 X (mm) 6.3 kN and reaction force R2 (right) = P 11.7 kN. Q 0.00Q/ 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
- 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 DyUNICARD Worksheet 10- Shear Force and Bending Moment Diagrams Question 3: (recommended time-30 minutes) Draw the shear force and bending moment diagrams for the beam given below. Determine the maximum bending moment in segment AB and its location from point A. Neglect the weight of the beam. Answer by following steps a to f, below. Ay 40 kN/m 20 kN B 150 kN·m 8 m 3 m a) Determine the support reactions at points A and B using the FBD of the entire beam. For OAx = 0 EM-0 +(By x8) (20 × 11)-(160 × 5,5)-150-0 By-152915 - (Ay +8) + (160 × 2,66)-150-60 = Ay 27.083 Ay Ax 5,3m 8m 160 20kN 150. b) How many segments are required to draw the shear and bending moment diagrams for the given beam? Name the segments. 2 Segments 5x 27,095 لاينا Segment SF 27,063 160 20 -5,3 Segment 152,915 Bending c) Express the shear force and bending moment as functions of x (the reference coordinate system is placed at point A) for segment AB and determine the shear force and bending moment at the points located…The simply supported beam is subjected to the force F = 700 N and the uniform distributed load with intensity w = 150 N/m. Draw the shear force and bending moment diagrams (in your homework documentation) and determine the equations for V(r) and M(x). Take a = 0 at point A. 19 F a Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 5.2 m 2.6 m 3.12 m Support Reactions The reaction at A is N. The reaction at D is N. Shear Force and Bending Moment Equations In section AB: V(x)= N and M(x)= N-m. In section BC: v(x)- N and M(x)= N-m. In section CD: V(x)- N and M(x)= N-m. A
- 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 w = 20.0 kips/ft, a=6.0 ft, and b=20.5 ft. 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 A B a W Calculate the reaction forces By and Cy 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 Bx = O, it has been omitted from the free-body diagram.) B b b X C XUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let o-1.5m.b=3.5 m.w=50 kN/m and P = 45 kN. 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. C Calculate the reaction forces A, and D, 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 A, -0, it has been omitted from the free-body diagram.) Answers: A, b KN, D, KN.1. Calculate reactions at the external supports. 2. Draw the free body diagram. 3. Build the diagrams if shear force and bending moment. (use the section method) 4. Find the diameter of section of the beam. 5. Calculate the maximum Tangential Stress and show the corresponding section. 6. Draw the stress distribution diagram in the most dangerous section of the beam. a (m) 4 b (m) | P (kN) q (kN/m) 1 80 8 A D-? [G] - 100 MPa a q B b P
- 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 XFor 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 XUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=4.0 m, b=2.5 m, PB = 4 kN, PC = 4 kN, and MB = 60 kN-m. 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.Calculate the reaction forces Ay and MA 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.) Determine the bending moment acting at each of the following locations:(a) x = 0+ m (i.e., just to the right of fixed support A)(b) x = 4.0– m (i.e., just to the left of B)(c) x = 4.0+ m (i.e., just to the right of B)(d) x = 6.5 mWhen entering your answers, use the bending moment sign convention.Answers:(a) M = kN-m.(b) M = kN-m.(c) M = kN-m.(d) M = kN-m.