1. Shear Force and Bending Moment (Solved Numerical) Kirtan
Adhikari Assistant Lecturer College of Science and Technology Royal
University of Bhutan [email protected] COLLEGE OF SCIENCE AND
TECHNOLOGY ROYAL UNIVERSITY OF BHUTAN RINCHENDING BHUTAN
18/3/2015
2. To understand the fundamental concept on Bending Moment and
Shear Force please read through text books (References). This ppt
contains step wise procedure to draw SFD and BMD 8/3/2015 2
Important Note
3. Draw SFD and BMD of the beam shown below. Indicate the
numerical values at all important point 8/3/2015 3 Question 1
4. a) For any type of questions start by computing support
reactions. b) Draw Free Body Diagram of the beam c) Convert UDL,
UVL to point load to compute support reaction. (only to compute
support reaction) 8/3/2015 4 Step 1 RA RB 8 4 2.5 2.52.5 1.25 1.255
5 4
6. Mark the point where Point load/support reaction acts or
points can be marked at the starting and ending of UDL/UVL In this
case the beam is divided into 4 portions AC, CD, DB and BE. Each
section has to be considered independently when calculating SF and
BM 8/3/2015 6 Step 3 Divide The Beam into portions
7. 7 Step 5 Draw a sectional line anywhere in portion AC x
Shear force at a sectional point (at a distance x from A) F = Ra
1*x Where (0 x 5) F = f(x).. This function produces straight line
graph (Linear Variation) Bending Moment at a sectional point (at a
distance x from A) BM = Ra*x 1*x * 2 Where (0 x 5) BM = f(x2).This
function Produces a Parabolic curve x
8. 8/3/2015 8 SFD & BMD for AC Shear Force = Ra x @ x = 0
10 kN @ x = 0.25 9.75 kN @ x = 0.5 9.5 kN @ x = 2.5 7.5 kN @ x = 5
5 kN Bending M = Ra*x 2 2 @ x = 0 0 kNm @ x = 0.25 2.47 kNm @ x =
0.5 4.88 kNm @ x = 2.5 21.88 kNm @ x = 5 37.5 kNm
9. 9 For Portion CD x x SF = Ra 1*5 8 BM = Ra*x 5*( x-2.5)
8*(x-5) Where (5 x 7.5) BM = f(x)Linear variation
10. 8/3/2015 10 SFD & BMD for CD Shear Force = Ra 5 8 @ x =
5 (C) -3 kN @ x = 7.5 (D) -3 kN Bending M =Ra*x 5*( x-2.5) 8*(x-5)
@ x = 5 (C) 37.5 kNm @ x = 5.25 36.75 kNm @ x = 5.75 35.25 kNm @ x
= 6 34.5 kNm @ x = 7.5 (D) 30 kNm
11. 11 For Portion DB x SF = Ra 1*5 8 - 4 BM = Ra*x 5*( x-2.5)
8*(x-5) 4(x-7.5) Where (7.5 x 12.5) BM = f(x)Linear variation
x
12. 8/3/2015 12 SFD & BMD for DB Shear Force = Ra 5 8 - 4 @
x = 7.5 (D) -7 kN @ x = 12.5 (B) -7 kN Bending M =Ra*x 17x + 82.5 @
x = 7.5 (D) 30 kNm @ x = 8.5 23 kNm @ x = 9.5 16 kNm @ x = 11.5 2
kNm @ x = 12.5 (B) -5 kNm
13. 13 For Portion BE SF = Ra 5 8 4 + Rb 1.6*(x-12.5) BM = Ra*x
5*( x-2.5) 8*(x-5) 4(x-7.5) + Rb * (x 12.5) 1.6 * (x-12.5) *
(x12.5) 2 BM = Ra*x + Rb * (x 12.5) 17x + 82.5 - 0.8 * (x 12.5)2
Where (12.5 x 1.5) BM = f(x2)Parabolic variation x(X- 5) m(X- 7. 5)
m(X- 12. 5) m
14. 8/3/2015 14 SFD & BMD for BE Shear Force = 24 - 1.6x @
x = 12.5 (B) 4 kN @ x = 14 1.6 kN @ x = 15 (E) 0 kN BM = 4x 55 -
0.8 * (x 12.5)2 @ x = 12.5 (B) -5 kNm @ x = 13 -3.2 kNm @ x = 13.5
-1.8 kNm @ x = 14 -0.8 kNm @ x = 15 (E) 0 kNm
15. Types of Loading Shape of Shear Force Diagram Shape of
Bending Moment Diagram Point Load Linearly Varying Graph (Straight
Line) Linearly Varying Graph (Straight Line) Uniformly Distributed
Load (UDL) Linearly Varying Graph (Straight Line) Parabolic Graph
(Smooth Curve) Uniformly Varying Load (UDL) Parabolic Graph (Smooth
Curve) Cubically varying Graph (Curve) 8/3/2015 15
Interpretations
16. 1. R.S.Khurmi. Strength of Materials. New Delhi: S.Chand
& Company Ltd. 2. Timoshenko, S.P., and D.H. Young (1993).
Elements of Strength of Materials.(5th Ed.).East West Press. 3.
Bhavikari, S. S., 2008. Strength of Materials. 3rd ed. Delhi: Vikas
Publishing House Pvt Ltd. 4. Ramamrutham, S. & Narayan, R.,
2009. Setrength of Materials. Noida: Dhanpat Rai Publishing Company
(P) Ltd 5. A.R.Jain and B.K.Jain (1987). Theory and Analysis of
Structures, Vol. Roorkee: Nemchand and Bros. 6. B.C.Punmia (1994).
Strength of Materials and Theory of Structures, Vol. 1. New Delhi:
Laxmi publications. 7. M. M. Ratwani & V.N.Vazirani (2008).
Analysis of Structure, Vol.1. New Delhi: Khanna Publishers. 8. R.K.
Bansal (1994). A Text Book on Strength of Materials. New Delhi:
Laxmi Publications. 9. R.K. Rajput.(2007). Strength of Materials.
New Delhi: S.Chand & Company Ltd 8/3/2015 16 References