4 5 singularity functions A systematic way to

4. 5 singularity functions • A systematic way to manage the concent. & discount. loading define as Ex) n=0 fn(x)=unit step ftn n=1 fn(x)=unit ramp ftn 2021 -02 -28 전남대학교 기계공학과 2

• To represent concentrated load & moment we introduce the new ftns as “Singularity functions” integration law 2021 -02 -28 전남대학교 기계공학과 4

해) P= a RA = a a RB= w Always, if loadings at boundary are include in q 2021 -02 -28 전남대학교 기계공학과 11

4. 6 computer method for SFD & BMD 1. Input : length of beam, L location of supports, a, c location of concentrated load, b value of concentrated load, -P 1 A. No. of points along the beam, N 2. Use of equil. Eqs. to determine the reaction RA, RB 3. Loading expression, q(x) 4. Shear force expression, V(x) 5. Bending moment expression, M(x) 6. Evaluate q(x), V(x), M(x) at points along the beam. 7. Plot q(x), V(x), M(x) 2021 -02 -28 전남대학교 기계공학과 16

4. 7 computer program to plot shear force & bending moment diagram 2021 -02 -28 전남대학교 기계공학과 18

4. 8 Three-dimensional problem 4. 2절의 general procedure적용 예 • General approach to determine the inter. force & moment 1. Idealize the actual problem 2. Use the equation of equil. to calculate any unknown reaction or support forces 3. Cut the member at a section of interest 2021 -02 -28 전남대학교 기계공학과 21

Ex 4. 25) Ducting internal force & moment at section C? neglecting the weight. 2021 -02 -28 전남대학교 기계공학과 22

Ex 4. 26) Internal force & moments at C? 2021 -02 -28 전남대학교 기계공학과 25