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=4.50 m, b=5.00 m, c= 2.75 m, P = 33kN and M = 195kN-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. 1.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.) (in kN) 2.Determine the shear force acting at each of the following locations: (in kN) (a) x = 4.50- (i.e., just to the left of point B) (b) x = 4.50+ (i.e., just to the right of point B) (c) x = 9.50- (i.e., just to the left of point C) (d) x = 9.50+ (i.e., just to the right of point C) Note that x = 0 at support A. 3. Determine the bending-moment acting at each of the following locations: (in kN-m) (a) x = 4.50- (i.e., just to the left of point B) (b) x = 4.50+ (i.e., just to the right of point B) (c) x = 9.50 m (i.e., at support C) (d) x = 8.50 m
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=4.50 m, b=5.00 m, c= 2.75 m, P = 33kN and M = 195kN-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.
1.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.) (in kN)
2.Determine the shear force acting at each of the following locations: (in kN)
(a) x = 4.50- (i.e., just to the left of point B)
(b) x = 4.50+ (i.e., just to the right of point B)
(c) x = 9.50- (i.e., just to the left of point C)
(d) x = 9.50+ (i.e., just to the right of point C)
Note that x = 0 at support A.
3. Determine the bending-moment acting at each of the following locations: (in kN-m)
(a) x = 4.50- (i.e., just to the left of point B)
(b) x = 4.50+ (i.e., just to the right of point B)
(c) x = 9.50 m (i.e., at support C)
(d) x = 8.50 m
Note that x = 0 at support A.
4. Use your bending-moment diagram to determine the maximum positive bending moment, Mmax, pos, and the maximum negative bending moment, Mmax, neg. Use the bending-moment sign convention detailed in Section 7.2. The maximum negative bending moment is the negative moment with the largest absolute value. Enter the maximum negative bending moment as a negative value.
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