Overhanged Beam and Cantilever beam problems

Overhanged Beam and Cantilever beam problems

1. Over hanged Beam Analysis for SFD and BMD By Venkata Sushma Chinta

2. Shear Force and Bending Moment Diagrams (SFD & BMD) Shear Force Diagram (SFD): The diagram which shows the variation of shear force along the length of the beam is called Shear Force Diagram (SFD). Bending Moment Diagram (BMD): The diagram which shows the variation of bending moment along the length of the beam is called Bending Moment Diagram (BMD).

3. Over hanged beam: If the end portion of a beam is extended beyond the support, such beam is known as overhanging beam. In case of overhanging beams, the B.M. is positive between the two supports, whereas the B.M. is negative for the over-hanging portion.

4. Point of Contra flexure [Inflection point]: It is the point on the bending moment diagram where bending moment changes the sign from positive to negative or vice versa. It is also called ‘Inflection point’. At the point of inflection point or contra flexure the bending moment is zero.

5. Q1. Draw the shear force and bending moment diagrams for the over-hanging beam carrying uniformly distributed load of 2 kN/m over the entire length as shown in Fig. Also locate the point of contraflexure

6. Estimate the reactions at supports: = 0 R A - + R B =0 R A + R B =     = 0 -12*3 + R B * 4 =0 R B * 4 = 36 R B =       R A = - R B R A = R A =   Force exerted by udl = 2*6=12 kN

7. Free body diagram of section1: 0< < 4 when x=0 section coincides with A, when x= 4 m section coincides with B   0< < 4 Section1-1 Shear force V= Bending Moment =0 (at A) V A = M A = = 0 = 4 (at B) V B =-5 M B = = -4 V B =-5 R A -2 - V=0 V = R A -2   - R A + M= R A - 2   = 0  

8. Free body diagram of section1: 0< < 4 when x=0 section coincides with A, when x= 4 m section coincides with B   0< < 4 Section1-1 Shear force V= Bending Moment =0 (at A) V A = M A = = 0 = 4 (at B) V B =-5 M B = = -4 = 1.5 m (at D) B.M max V D =0 M D = = 2.25 =3 m (at E) B.M zero V E =3-2*3=-3 M E = = 0 V B =-5 V D =0 V E =3-2*3=-3 V = Shear force is zero at => = 1.5 m   M= 3 - 2 Shear force is zero at 3 - 2 =0 => =0, =3;  

9. 0< < 2 Section2-2 Shear force V= Bending Moment =0 (at C) V C =2*0=0 M C = = 0 = 2 (at B) V B =2*2=4 M B = = -4 V C =2*0=0 V B =2*2=4

10. 0< < 4 Section1-1 Shear force Bending Moment =0 (at A) V A = M A = = 4 (at B) V B =-5 M B = -4 = 1.5 m (at D) B.M max V D =0 M D = 2.25 =3 m(at E) B.M zero V E =-3 M E = Shear force Bending Moment M A = V B =-5 M B = -4 V D =0 M D = 2.25 V E =-3 M E = 0< < 2 Section2-2 Shear force V= Bending Moment =0 (at C) V C =0 M C = = 2 (at B) V B =4 M B = -4 V C =0 M C = V B =4 M B = -4

11. Q2. Draw the S.F. and B.M. diagrams for the beam which is loaded as shown in Fig. Determine the points of contraflexure within the span AB.

12. Estimate the reactions at supports: = 0 R A + R B =800+2000+1000 R A + R B =     = 0 800*3-2000*5+ R B *8-1000*10 =0 R B *8= 10000+10000-2400 R B = 2200       R A = - R B R A = R A = 1600 N  

13. Point of contraflexure M=0 800 – 4800 =0 = 6 m   3< < 8 Section1-1 Shear force V= Bending Moment =3 (at A) V A =800 M A = -2400 = 8 (at D) V D =800 M D = = 1600 V A =800 V D =800

14. Point of contraflexure M=0 1200 – 4400 =0 = 3.7 m   2< < 5 Section2-2 Shear force V= Bending Moment =2 (at B) V B =-1200 M B = -2000 = 5 (at D) V D =-1200 M D = = 1600 V B =-1200 V D =-1200

15. Cantilever Beam Analysis for SFD and BMD

16. Cantilever Beam A  cantilever  is a rigid  structural element  that extends horizontally and is supported at only one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a cantilever can be formed as a  beam , plate,  truss , or  slab .

17. Pamban Bridge in Rameswaram is an engineering marvel. It is India’s first Cantilever bridge

18. Cantilever car parking roof

19. Traffic signal Post

20. Busan Cinema Center  in Busan, South Korea, with the world's longest cantilever roof.

21. The pioneering  Junkers J 1  all-metal monoplane of 1915, the first aircraft to fly with cantilever wings

22. Q1. Shear force and bending moment diagrams for a cantilever with a point load at the free end

23. Q2.A cantilever beam of length 2 m carries the point loads as shown in Fig.. Draw the shear force and B.M. diagrams for the cantilever beam

24. Q3. Shear force and bending moment diagrams for a cantilever with a UNIFORMLY DISTRIBUTED LOAD through out its length

25. Q4. A cantilever of length 2.0 m carries a uniformly distributed load of1 kN/m run over a length of 1.5 m from the free end. Draw the shear force and bending moment diagrams for the cantilever

26. Q5. A cantilever of length 2 m carries a uniformly distributed load of 1.5 kN/m run over the whole length and a point load of2 kN at a distance of 0.5m from the free end. Draw the S.F. and B.M. diagrams for the cantilever.

27. Q5. A cantilever of length 2 m carries a uniformly distributed load of 1.5 kN/m run over the whole length and a point load of2 kN at a distance of 0.5m from the free end. Draw the S.F. and B.M. diagrams for the cantilever.