Problem 1 Solve the reactions for the beam and draw the shear & moment diagram. 60 kN 120 kN – m 20 kN/m A В D E 2 m 2 m 2 m 2 m Determine the following: 1. Reaction at B. 2. Reaction at E 3. Maximum shear. 4. Maximum positive moment. 5. Maximum negative moment
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- 1 / 2 118% Problem 1 Solve the reactions for the beam and draw the shear & moment diagram. 60 kN 120 kN – m 20 kN/m A В C D E 2 m 2 m 2 m 2 m Determine the following: 1. Reaction at B. (5 pts) 2. Reaction at E (5 pts) 3. Maximum shear. (10 pts) 4. Maximum positive moment. (10 pts) 5. Maximum negative moment (10 pts)PROBLEM 2 For the beam shown, determine the reactions at A, B and D. At B, C and D is a pin and at A is a fixed support. The uniformly varying load has an intensity of .6 k/ft. 13k 6.k qk -3k -6k/4 11 D g 8² g² 15determine the reaction R1. determine the reaction R2. determine the shear at point 4meters from R1 determine the moment at point 4 meters from R1. determine the maximum moment on the beam
- 3) A triangular cross section beam of 6m length is fixed at its two sides A and B. From support A to the centre of the beam the triangular cross section has equal sides of 100mm and from the centre to B the triangular cross section has equal sides of 300mm. Fixed support B allows a rotation of 0.02 radians in any direction. Determine the reactions at A and B if there is torsion moment load of 4kN.m working in the centre of the first half of the beam. _Given that the polar moment of inertia for any shape is given by the equation J = lx + ly, where I is the moment of inertia of the section. The base of the triangle is always horizontal for the cross sections. The length of the beam is 4m and G = 80GPA. Hence determine the maximum shear stress in the beam. bh bh 36 h/3 36a). What is the reaction at R1? (in kN) b). What is the reaction at R2? (in kN) c).What is the absolute maximum shear in the beam? (in kN) d.)What is the location of the absolute maximum shear from the left end of the beam? (in m) e).What is the absolute maximum moment in the beam? (in kNm) f).What is the location of the absolute maximum moment from the left end of the beam? (in m) g).What is the moment of inertia (I) about the neutral axis of the section? (in mm^4) h).What is the first moment of an area (Q) about the neutral axis of the section? (in mm^3) i).What is the maximum shearing stress (fv) of the beam? (in MPa) j).What is the maximum flexural stress (fb) of the beam? (in MPa)Need the Solution: Determine the maximum reaction at support B, the maximum shear at point C and the maximum positive moment that can be developed at point C on the beam shown due to: -a single concentrate live load of 8000 N [Ans: By = 49,111.11 N] -a uniform live load of 3000N/m (applied on specific area: say positive area or negative area only) [Vcmax= -9277.78 N] -a beam weight (dead load) of 1000N/m (applied on the entire beam) [+Mcmax= 54,222.22 N-m]
- Q1 a: Calculate the reactions at the supports A and E. b: Draw the shear force diagram. c: Draw the bending moment diagram. d: Draw the deflected shape. 200 kNm 100 kN 50 kN/m F D E 3 m SFD (kN) BMD (kNm) Deflected shapeI. The reaction at support B RBy II The reaction at support C RCy III. The bending moment at B IV. The maximum absolute value of the shear force in the beam V. Draw the shear force and bending moment diagram for the beam2. The hinge at E connects beams AE and EH to form the compound beam. The support at A is pinned and the other supports are rollers. Determine a) b) The reactions at A, D, and H; The shear diagram; The moment diagram. 300 N A 300 N 50 N B†C D E 300 N FG Hinge 7 @ 220 mm = 1540 mm - H
- Determine the maximum reaction at support B, the maximum shear at point C and the maximum positive moment that can be developed at point C on the beam shown due to: "a single concentrate live load of 8000N "a uniform live load of 3000 N/m (applied on specific area: say positive area or negative area only) "a beam weight (dead load) of 1000 N/m (applied on the entire beam) A C B 4 m 5 m 4 mThe L-shaped body is supported by a roller at B and a frictionless pin at A. The body supports a 250 lb ver- tical force at C and a 500 ft-lb couple- moment at D. Determine the reactions at A and B.a.) What is the reaction at R1? (in kN) b.) What is the reaction at R2? (in kN) c.) What is the absolute maximum shear in the beam? (in kN) d.) What is the location of the absolute maximum shear from the left end of the beam? (in m) e.) What is the absolute maximum moment in the beam? (in kNm) f.)What is the location of the absolute maximum moment from the left end of the beam? (in m) g.)What is the moment of inertia (I) about the neutral axis of the section? (in mm^4) h.)What is the first moment of an area (Q) about the neutral axis of the section? (in mm^3) i.)What is the maximum shearing stress (fv) of the beam? (in MPa) j.)What is the maximum flexural stress (fb) of the beam? (in MPa) Note: Please draw free body diagram and answer all letters.