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- UNICARD 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…60 kN 12 kN/m 200 kN.m Ca B 5 m A -5 m -10 m- 5 m- 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 d) Write functions for bending moment (M) in terms of x. Draw Shear Force Diagram (SFD) for whole beam f) Draw Bending Moment Diagram (BMD) for whole beam g) Determine the maximum moment Mmax With its locationforce, the sign convention is same as that used in lectures and seminars). A simply supported beam is loaded as shown in the Figure. The corresponding SFD and BMD would be: 20 kN 10 kN/m 2 m 2 m 30 kN (a) 40 kN m 30 kN 30 kN 10 kN (b) 40 kN.m 10 kN 30 kN 30 kN Click Save and Submit to save and submit. Click Save All Answers to save all answvers.
- Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=4.0 ft, b-9.0 ft. c=4.0 ft, d=3.0ft, w=8 kips/ft and P = 66 kips. 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. B B ÎÎÎÎÎÎ Answers: Ay=i b d For this loading, calculate the reaction forces Ay and Ey 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.) W C b C C D E kips, Ey = i E X Ey kips.Use 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.Question 4 Sketch bending moment diagram for the loading acting on the beam as shown in Figure Q4. From your results, calculate area required for tensile reinforcement using M the formula 4, You may use fyk = 500 MPa and z = 1400 mm. 0.87 fyk 90 kN/m 30 kN/m 200 KN 20 kN/m Danim 100 kNm 2m 5m 3m Figure Q4
- 3- Draw the shear force and bending moment of the beam. You have to find their equation, and your diagram without calculation is not acceptable.(41) 20 kN 1.5 kN/m B 1m 1 m 4 mPART 1 Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=3.5 m, b=2.0 m, PB = 2 kN, PC = 2 kN, and MB = 20 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. IMAGE* 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.) IMAGE* PART 2 Determine the shear force acting at each of the following locations:(a) x = 0+ m (i.e., just to the right of fixed support A)(b) x = 3.5– m (i.e., just to the left of B)(c) x = 3.5+ m (i.e., just to the right of B)(d) x = 5.5– m (i.e., just to the left of C)When entering your answers, use the shear force sign convention.Answer:(a) V = ? kN.(b) V = ? kN.(c) V = ? kN.(d) V = ? kN. PART 3…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 Dy
- 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. y A A Answers: By a = 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.) = a i B Cy i = W B b W b kips X kips X3. a) Develop the shear force and bending moment equations for each section. b) Sketch the shear force and bending moment diagrams for the beam and label the values of shear force and bending moment at the important points. q-2 kN/m A 2 m 2m Figure Q3 M-5 kNm 2mUse the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=3 ft, b-9 ft, c=2 ft and w=10.5 kips/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. B Ay B b Answers: Ay = i Calculate the reaction forces Ay 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 Ax = 0, it has been omitted from the free-body diagram.) W b CS W C₁ Cy с D kips, Cy= i kips.