Bending Moment 1. CH28 p355 How to find Bending Moment Calculate BM: M = Fr (Perpendicular to the force) Bending moment is a torque applied to each side of the beam if it was cut in two - anywhere along its length. The hinge applies a clockwise (+) moment (torque) to the RHS, and a counter-clockwise (-) moment to the LHS. Example Bending-Moment Page 1
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How to find Bending Moment Bending Moment 1. CH28 p355mem50212.com/MDME/MEMmods/MEM30006A/Bending_Moment/N… · Calculate BM: M = Fr (Perpendicular to the force) In equilibrium,
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Bending Moment 1.
CH28 p355How to find Bending Moment
Calculate BM: M = Fr (Perpendicular to the force)
Bending moment is a torque applied to each side of the beam if it was cut in two - anywhere along its length.The hinge applies a clockwise (+) moment (torque) to the RHS, and a counter-clockwise (-) moment to the LHS.
Example
Bending-Moment Page 1
Calculate BM: M = Fr (Perpendicular to the force)
In equilibrium, so MA = 0But to find the Bending Moment, you must cut the beam in two.Bending moment is INTERNAL, moment is EXTERNAL.
BM for RHS of beam:M = Fr = -(6*3) = -18 kNm
Repeat for LHS:M = Fr = (6*3) = 18 kNm
Procedure to find BM at any cross-section in the beam:Cut beam thru that section, then add moments for the right or left side only. Ignore + or - sign, and use the following definition for +/-;
Positive = sagging Negative = hogging
A good way to double-check is to do moments for BOTH sides and compare.
In engineering, we are concerned with the MAXIMUM BM.How do we find it?
Try the same problem at 1m from left end;
Bending-Moment Page 2
BM for LHS of beam:M = Fr = (6*1) = 6 kNm
Repeat for RHS:M = Fr = +(12*2) -(6*5) = -6 kNm
The BMD helps us know the MAXIMUM, but also what the BM is an any location along the beam.
Bending-Moment Page 3
Q1: If distance a=7.8m and Force b=9.3kN, find the maximum bending moment. Sag=(+), Hogg=(-)
Check the max BM:Take section thru centre:Moment LHS = +(3*1.75) -(3*0.75) = 3.0 Moment RHS = -(3*1.75) +(3*0.75) = -3.0 We cannot determine +/- from the moment equation because it depends which side we choose.Positive bending moment = SAGGINGNegative bending moment = HOGGING
The SFD (Shear Force Diagram) tells you how much the beam wants to SLIDE apart.
The BMD (Bending Moment Diagram) tells you how much the beam wants to BEND apart by rotation.
Bending-Moment Page 9
M = + (5*4) -12 = 8 kNm
M = - (4*2) = -8 kNm
Example 28.1 h
The area of the SFD = height of the BMD
Positive Shear Force
Positive Bending Moment
The maximum bending moment = 12The maximum negative BM = -8
Remember!You can't determine + or - by looking at the RHS or LHS, since they will always be opposing each other.
Just use sagging = positive bending.
Wall Reaction:M = -(4*8)+(9*6)-(5*2) = 12So wall reaction moment is -12 (CCW)
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SFD from LHS:Starts at -2 because down on LHS.
BMD from LHS:Starts at 0 because free end on beam. Max at 2 places..
Example 28.1(j)Tuesday, 20 March 20126:11 PM
Bending-Moment Page 11
Get reactions:Find Volume:V = 0.14*0.26*12 = 0.4368 m3
M = *V = 7150*0.4368 = 3123.12 kgReactions = 3123.12*9.81/2 = 15318.9 N = 15.3189 kNArea in SFD = BMBM = 0.5*15.3*6 = 45.9 kNm
Check by cutting in half and find Moment: = 3123.12 /2 = 1561.56 kg = 15.3189 kNMoment = +(15.3*3)- (15.3*6) = -45.9 kNmForget the minus sign when you cut in half because you get a different sign depending on which side you take!Scrap minus sign and use HOGG/SAG.