UNIT II Shear Force Diagrams and Bending Moment

UNIT II Shear Force Diagrams and Bending Moment Diagrams Lecture Number -3 Prof. M. J. Naidu Mechanical Engineering Department Smt. Kashibai Navale College of Engineering, Pune-41 Strength of Materials

Illustrative Numerical 1 For the beam and loading shown, draw the shear and bend-moment diagrams.

HINTS • • • Apply the elastic flexure formulas Determine the corresponding maximum normal stress. Treating the entire beam as a rigid body Determine the reaction forces Identify the maximum shear and bending-moment from plots of their distributions.

Solution • Reaction forces RB =40 k. N RD =14 k. N • Applying equilibrium analyses on resulting free-bodies -20 - V 1=0 , V 1= -20 k. N 20*0 + M 1=0 , M 1=0 k. N. m -20 – V 2=0 , V 2= -20 k. N 20*2. 5 + M 2=0 , M 2=50 k. N. m V 3= +26 k. N M 3=-50 k. N. m V 4= +26 k. N M 4=+28 k. N. m V 5= -14 k. N M 5=+28 k. N. m V 6= -14 k. N M 6=0 k. N. m

SFD and BMD

Illustrative Numerical : 2 Draw SFD and BMD for the beam shown

Illustrative Numerical : 2 … • • • Solution: Using equation of statics: RAy=15 N and RBy= 35 N V at A = 15 k. N V just before B = – 15 N V just after B = 20 N V between B and C = 20 N M at A= 0 M at B= 0 M at C= 80 N-m Mmax = 22. 5 N-m

Illustrative Numerical : 2…

Workout Numerical Draw SFD and BMD of figure shown.