Homework Answers
The solution is provided in the images below. You need to first find the reaction forces at the supports A and B. After that, we proceed with finding the value of shear force and bending moment by taking a section at distance 3m from A. Revert back in case of any query.
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Beam AB with loading as shown
Find: a) V (x=3); b) M (x=3).
PS 14-2 Given:...
For the loading shown in the below figure, knowing that wo 2 kN/m, the length of the beam is L 2 ...
For the loading shown in the below figure, knowing that wo 2 kN/m, the length of the beam is L 2 m, and the bending rigidity EI-204 kN-m2, a) Find the deflection equation for the beam by integration. Clearly specify the conditions to determine the constants of integration b) Find the vertical force needed at point A to prevent vertical displacement at point A (v(0)-0) c) Find the moment needed at point A to have zero slope at point A...
A cantilever beam AB is subjected to a triangle loading with concentrated moment (see figure). The...
A cantilever beam AB is subjected to a triangle loading with concentrated moment (see figure). The moment curvature equation is shown (from the left). (El=constant) 1. Determine the deflection at point A. 2. Determine the rotation at point A. 3 kN/m 15 kN-m A B 6 m d2v ΕΙ 5x3 3 x2 – 15 2 dx2 6
2. For the beam and loading shown in the following figure: (a) find all the reaction...
2. For the beam and loading shown in the following figure: (a) find all the reaction forces, (b) draw the shear and bending moment diagrams and (c) determine the maximum absolute value of the shear and the bending moment. 25 kN m 40 kN 401N 0.61 1.S 0.6 m
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature...
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature equation is shown (from the left). The (El-constant) 1. Determine the deflection at middle beam. 2. Determine the rotation at middle beam. 2 kN/m B 4 m 8 EI 12 MacBook Air DOO 008 A tA % A - 5 & 7 6 I 0 * 8 9 R T
Acantilever beam AB is subjected to a triangle loading with concentrated moment (see figure). The moment...
Acantilever beam AB is subjected to a triangle loading with concentrated moment (see figure). The moment curvature equation is shown (from the left). (El=constant) 1. Determine the deflection at point A. 2. Determine the rotation at point A. 3 kN/m 15 kN-m B 6 m d2v EI dx- 5x3 3 --x2 - 15 6 2
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature...
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature equation is shown (from the left). The (El-constant) 1. Determine the deflection at middle beam. 2. Determine the rotation at middle beam. 2 kN/m A B 4.m x3 EI dx2 = - 2 COM MacBook Air 20 COD F4 FS F6 ►II # $ دیا 4 % 5 6 & 7 8 9
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature...
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature equation is shown (from the left). The (El=constant) 1. Determine the deflection at middle beam. 2. Determine the rotation at middle beam. 2 kN/m A B 4 m d2v x3 ΕΙ = dx? 12 -x2+1
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature...
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature equation is shown (from the left). The (El=constant) 1. Determine the deflection at middle beam. 2. Determine the rotation at middle beam. 2 kN/m A B 4 m 8 d2v EI dx2 x3 12 *+z*
2. For the beam and loading shown, design the cross section of the beam, knowing that...
2. For the beam and loading shown, design the cross section of the beam, knowing that the grade of timber used has an allowable normal stress of 12 MPa 2.5 KN 2.5 KN 100 mm 6 kN/m 0.6 m 0.6 m 3. Knowing that the allowable normal stress for the steel used is 160 MPa, select the most economical S shape beam to support the loading shown. SO KN 100 kN/m B 0.8m- 1.6 m
QUESTION 1 [15] For the simply supported beam subjected to the loading shown in the figure,...
QUESTION 1 [15] For the simply supported beam subjected to the loading shown in the figure, a) Derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) b) Report the maximum positive bending moment, the maximum negative bending moment, and their respective locations. 36 KN 180 KN-m X B C D 4 m 5 m 3 m Figure 1
For the loading shown in the below figure, knowing that wo 2 kN/m, the length of the beam is L 2 m, and the bending rigidity EI-204 kN-m2, a) Find the deflection equation for the beam by integration. Clearly specify the conditions to determine the constants of integration b) Find the vertical force needed at point A to prevent vertical displacement at point A (v(0)-0) c) Find the moment needed at point A to have zero slope at point A...
A cantilever beam AB is subjected to a triangle loading with concentrated moment (see figure). The moment curvature equation is shown (from the left). (El=constant) 1. Determine the deflection at point A. 2. Determine the rotation at point A. 3 kN/m 15 kN-m A B 6 m d2v ΕΙ 5x3 3 x2 – 15 2 dx2 6
2. For the beam and loading shown in the following figure: (a) find all the reaction forces, (b) draw the shear and bending moment diagrams and (c) determine the maximum absolute value of the shear and the bending moment. 25 kN m 40 kN 401N 0.61 1.S 0.6 m
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature equation is shown (from the left). The (El-constant) 1. Determine the deflection at middle beam. 2. Determine the rotation at middle beam. 2 kN/m B 4 m 8 EI 12 MacBook Air DOO 008 A tA % A - 5 & 7 6 I 0 * 8 9 R T
Acantilever beam AB is subjected to a triangle loading with concentrated moment (see figure). The moment curvature equation is shown (from the left). (El=constant) 1. Determine the deflection at point A. 2. Determine the rotation at point A. 3 kN/m 15 kN-m B 6 m d2v EI dx- 5x3 3 --x2 - 15 6 2
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature equation is shown (from the left). The (El-constant) 1. Determine the deflection at middle beam. 2. Determine the rotation at middle beam. 2 kN/m A B 4.m x3 EI dx2 = - 2 COM MacBook Air 20 COD F4 FS F6 ►II # $ دیا 4 % 5 6 & 7 8 9
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature equation is shown (from the left). The (El=constant) 1. Determine the deflection at middle beam. 2. Determine the rotation at middle beam. 2 kN/m A B 4 m d2v x3 ΕΙ = dx? 12 -x2+1
A simply supported beam AB is subjected to a triangle loading (see figure). The moment curvature equation is shown (from the left). The (El=constant) 1. Determine the deflection at middle beam. 2. Determine the rotation at middle beam. 2 kN/m A B 4 m 8 d2v EI dx2 x3 12 *+z*
2. For the beam and loading shown, design the cross section of the beam, knowing that the grade of timber used has an allowable normal stress of 12 MPa 2.5 KN 2.5 KN 100 mm 6 kN/m 0.6 m 0.6 m 3. Knowing that the allowable normal stress for the steel used is 160 MPa, select the most economical S shape beam to support the loading shown. SO KN 100 kN/m B 0.8m- 1.6 m
QUESTION 1 [15] For the simply supported beam subjected to the loading shown in the figure, a) Derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) b) Report the maximum positive bending moment, the maximum negative bending moment, and their respective locations. 36 KN 180 KN-m X B C D 4 m 5 m 3 m Figure 1
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