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8 KN + 120 kN.m Uc Up 10 m 20 m Loading Loading Function w =...
8 KN + 120 kN.m Uc Up 10 m 20 m Loading Loading Function w = w(x) Shear V =%w(x)dx Moment M = /Vdx (1) M w= M.(x-a) 2 V = M.(x-a)" M M.(x-4) (2) V - P(x-a) M - P(x-a)' (3) WO WO V = wo(x-a)' M slope = m w = m(x-a)' M = " (x-a)" Using Macaulay functions, determine the moment equation of the beam above. o -8 <2-0>1 +6<< -10 >1 o --8<-0> +6<< -10 >...
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...
Question 1: (20 Points) For the beam and loading shown: a- Draw shear and moment diagrams. b- Write equations of shear and moment for all segments of the beam from 20 kN 0 kN 8 kN/m x =-4 to x = 8, U...
Question 1: (20 Points) For the beam and loading shown: a- Draw shear and moment diagrams. b- Write equations of shear and moment for all segments of the beam from 20 kN 0 kN 8 kN/m x =-4 to x = 8, Use x-y axes as shown. Do not change x-y coordinates. Answers: M56 kN-mx4.09 kN-m
Question 1: (20 Points) For the beam and loading shown: a- Draw shear and moment diagrams. b- Write equations of shear and moment for...
Q5. The cantilever beam, AC, is subjected to the load case shown in Figure 5. For the loading shown, do the following: [10 Marks] a) Calculate the magnitude and direction of the reactions at A b) Usi...
Q5. The cantilever beam, AC, is subjected to the load case shown in Figure 5. For the loading shown, do the following: [10 Marks] a) Calculate the magnitude and direction of the reactions at A b) Using the Macaulay function, determine the displacement in y of the point B of the beam (x 2.4 m from the support at A) [10 Marks] c) Determine the slope at B. [5 Marks] The beam has a Young's modulus of E-200 GPa and...
2. The governing differential equation that relates the deflection y of a beam to the load w ia w...
2. The governing differential equation that relates the deflection y of a beam to the load w ia where both y and w are are functions of r. In the above equation, E is the modulus of elasticity and I is the moment of inertia of the beam. For the beam and loading shown in the figure, first de m, E = 200 GPa, 1 = 100 × 106 mm4 and uo 100 kN/m and determine the maximum deflection. Note...
8. The cantilever beam in Figure Q8 subjects to concentrated loading. The cross section geometry gives...
8. The cantilever beam in Figure Q8 subjects to concentrated loading. The cross section geometry gives the second moment of area / 100 x 10 m. The longitudinal geometry of the beam: a 2 m, b 1 m. The material of the beam: Young's modulus E 200 GPa. The loading: concentrated force P 10 KN. (a) Determine the reactions to the beam at the fixed end. (b) Determine the rotation angle at point x-a (c) (Determine the deflection at the...
The steel beam has the configuration, loading pattern and cross-sectional area shown in Figure 8. Assuming w = 5 kN/m, d...
The steel beam has the configuration, loading pattern and
cross-sectional area shown in Figure 8.
Assuming w = 5 kN/m, determine:
a) the reactions at each end of the beam
b) the second moment of area of the section about the relevant
axis of bending
c) the maximum shear stress and associated distribution of shear
stresses in the beam
d) the maximum bending stress and distribution of bending
stresses in the beam
0.8 m 0.8 m 0.8 m 8 cm...
Problem 1. Establish the loading and moment functions for the beam using singularity functions. W max...
Problem 1. Establish the loading and moment functions for the beam using singularity functions. W max = 2 kN/m L WR = 1 kN/m TIITT - - >X 4 m- 4 m Problem 2. Take E=150 GPa and I=65x109 mm .Determine the maximum deflection of the beam. Use singularity functions. 2.20kN 800 N k am *2m ***227
For the following loading diagram, determine the most economical size based upon the loading diag...
structural calculations
For the following loading diagram, determine the most economical size based upon the loading diagram. Apply the bending coerricitent and then determine the required sized based upon the effective moment. Loads are unfactored and the beam weight is included in the unit weights. LL = 50 K LL = 1 K/Ft 10'-0" 10-0" 15'-0 blem 3 Required Beam Size before applying bending coefficient: Mc MMAx Cb- Required Beam Size after applying bending coefficient 5. SIMPLE BEAM-UNIFORM LOAD PARTIALLY...
1. For the simply supported beam subjected to the loading shown, Derive equations for the shear...
1. 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.) a. b. Plot the shear-force and bending-moment diagrams for the beam using the derived functions c. Report the maximum bending moment and its location. 42 kips 6 kips/ft 10 ft 20 ft
8 KN + 120 kN.m Uc Up 10 m 20 m Loading Loading Function w = w(x) Shear V =%w(x)dx Moment M = /Vdx (1) M w= M.(x-a) 2 V = M.(x-a)" M M.(x-4) (2) V - P(x-a) M - P(x-a)' (3) WO WO V = wo(x-a)' M slope = m w = m(x-a)' M = " (x-a)" Using Macaulay functions, determine the moment equation of the beam above. o -8 <2-0>1 +6<< -10 >1 o --8<-0> +6<< -10 >...
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...
Question 1: (20 Points) For the beam and loading shown: a- Draw shear and moment diagrams. b- Write equations of shear and moment for all segments of the beam from 20 kN 0 kN 8 kN/m x =-4 to x = 8, Use x-y axes as shown. Do not change x-y coordinates. Answers: M56 kN-mx4.09 kN-m
Question 1: (20 Points) For the beam and loading shown: a- Draw shear and moment diagrams. b- Write equations of shear and moment for...
Q5. The cantilever beam, AC, is subjected to the load case shown in Figure 5. For the loading shown, do the following: [10 Marks] a) Calculate the magnitude and direction of the reactions at A b) Using the Macaulay function, determine the displacement in y of the point B of the beam (x 2.4 m from the support at A) [10 Marks] c) Determine the slope at B. [5 Marks] The beam has a Young's modulus of E-200 GPa and...
2. The governing differential equation that relates the deflection y of a beam to the load w ia where both y and w are are functions of r. In the above equation, E is the modulus of elasticity and I is the moment of inertia of the beam. For the beam and loading shown in the figure, first de m, E = 200 GPa, 1 = 100 × 106 mm4 and uo 100 kN/m and determine the maximum deflection. Note...
8. The cantilever beam in Figure Q8 subjects to concentrated loading. The cross section geometry gives the second moment of area / 100 x 10 m. The longitudinal geometry of the beam: a 2 m, b 1 m. The material of the beam: Young's modulus E 200 GPa. The loading: concentrated force P 10 KN. (a) Determine the reactions to the beam at the fixed end. (b) Determine the rotation angle at point x-a (c) (Determine the deflection at the...
The steel beam has the configuration, loading pattern and
cross-sectional area shown in Figure 8.
Assuming w = 5 kN/m, determine:
a) the reactions at each end of the beam
b) the second moment of area of the section about the relevant
axis of bending
c) the maximum shear stress and associated distribution of shear
stresses in the beam
d) the maximum bending stress and distribution of bending
stresses in the beam
0.8 m 0.8 m 0.8 m 8 cm...
Problem 1. Establish the loading and moment functions for the beam using singularity functions. W max = 2 kN/m L WR = 1 kN/m TIITT - - >X 4 m- 4 m Problem 2. Take E=150 GPa and I=65x109 mm .Determine the maximum deflection of the beam. Use singularity functions. 2.20kN 800 N k am *2m ***227
structural calculations
For the following loading diagram, determine the most economical size based upon the loading diagram. Apply the bending coerricitent and then determine the required sized based upon the effective moment. Loads are unfactored and the beam weight is included in the unit weights. LL = 50 K LL = 1 K/Ft 10'-0" 10-0" 15'-0 blem 3 Required Beam Size before applying bending coefficient: Mc MMAx Cb- Required Beam Size after applying bending coefficient 5. SIMPLE BEAM-UNIFORM LOAD PARTIALLY...
1. 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.) a. b. Plot the shear-force and bending-moment diagrams for the beam using the derived functions c. Report the maximum bending moment and its location. 42 kips 6 kips/ft 10 ft 20 ft
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