class #26
DESCRIPTION
Class #26. Beams Shear and Bending Moment Diagrams Statics Spring 2006 Dr. Pickett. Steps for V and BM diagrams. 1.Draw FBD 2.Obtain reactions: S M (@left support) to obtain vertical reaction at right; S M (@Right support) to obtain vertical reaction at left; Check S Fy = 0 - PowerPoint PPT PresentationTRANSCRIPT
11
Class #26Class #26
BeamsBeams
Shear and Bending Moment Shear and Bending Moment DiagramsDiagrams
StaticsStatics
Spring 2006Spring 2006
Dr. PickettDr. Pickett
22
Steps for V and BM diagramsSteps for V and BM diagrams
1.Draw FBD1.Draw FBD
2.Obtain reactions:2.Obtain reactions:
M (@left support) to obtain vertical reaction at right;M (@left support) to obtain vertical reaction at right;
M (@Right support) to obtain vertical reaction at left;M (@Right support) to obtain vertical reaction at left;
Check Check Fy = 0 Fy = 0
Check Check ∑Fx = 0∑Fx = 0
3. Cut a section ;3. Cut a section ;
Obtain internal P,V,M at cut section ;Obtain internal P,V,M at cut section ;
M, M, Fy, Fy, FxFx
4. Record, draw internal P, V, M on both sides of cut sections ;4. Record, draw internal P, V, M on both sides of cut sections ;
-- magnitudemagnitude
-- unitsunits
-- direction on both sides of cutdirection on both sides of cut
33
Using Engineering Activities To Teach Math & Science
44
7.627.62
0
0
AX
AXX
R
RF
C
LBFTLBFTC
FT
FTFTFT
LBFTLBFT
CA
R
R
RM
LB
1800
324005400150
2
998009600150
LB
LBFT
FT
AY
LBFTFTAY
FTLbFT
FTLBFTAYC
R
R
RM
4800
36007560015
66002
969800150
LBLB
FTFT
LBLBLB
Y
LB
F
720072000
9800600480018000
55
7.62 contd7.62 contd
EndLeftfromftxM LBFTMAX .........6....14400
FT
FTFT
LBLB
LBFTFT
LB
BA
x
xV
V
6
80048000
72009800
FtLbFtLb
FtLbFTLB
FtLbFtLbFtLb
FtLbFTLB
FtLbFTLB
M
M
M
M
M
1080010800
1080061800
10800360014400
3600324002
1
14400648002
1
'15
'15'9
'9
'9'6
'60
3 ft
Max Moment occurs at the location where shear is zero
66
7.62 contd7.62 contd
EndLeftfromftxM LBFTMAX .........6....14400
LbLBLbxx
Lbftx
FTFT
LBLB
Ft
LbLb
xx
VVV
V
x
dxVVV
180006002400
2400
8004800
8004800
159159
9090
9
9
9
0
0
3 ftdxxMMM
M
Ft
LbLb
xx
9
0
0
0
80048000
0
9090
LbFtLbFtLbFtftx
FtLbLb
M
xx...
9
2
108003240043200
4004800
xdxMMM LbLbFtLbLbFtxx )1800(10800180010800 .12
9
.9 129129
LbFtLbFtftxM
..12 1080010800
77
Steps for V and BM diagramsSteps for V and BM diagrams
1.Draw FBD1.Draw FBD
2.Obtain reactions:2.Obtain reactions:
M (@left support) to obtain vertical reaction at right;M (@left support) to obtain vertical reaction at right;
M (@Right support) to obtain vertical reaction at left;M (@Right support) to obtain vertical reaction at left;
Check Check Fy = 0 Fy = 0
Check Check ∑Fx = 0∑Fx = 0
3. Cut a section ;3. Cut a section ;
Obtain internal P,V,M at cut section ;Obtain internal P,V,M at cut section ;
M, M, Fy, Fy, FxFx
4. Record, draw internal P, V, M on both sides of cut sections ;4. Record, draw internal P, V, M on both sides of cut sections ;
-- magnitudemagnitude
-- unitsunits
-- direction on both sides of cutdirection on both sides of cut
88
7.707.70
Moments at A and C have been Moments at A and C have been experimentally measured as:experimentally measured as:
Find P and QFind P and Q
NmC
NmA
M
M
215
395
AN
Nmm
NNmm
A
Nmmmm
NNmm
AACC
V
V
VM
1000
215203952.00
2151.02.010003952.00
99
7.70 Contd7.70 Contd
P
P
PM
N
mNmNmNm
mmmmm
NmNNm
ABB
300
25.01806503950
25.02.025.04.0100065.010003950
Q
Q
QM
N
mNmNmNm
mmmm
NmNNm
ABO
300
65.0801203950
65.02.04.010004.03003950
1010
Nmm
N
DC
Nmm
N
CA
V
V
2002.0*1000
2002.0*1000
NmmNmNCAM 1802.0200
2
12.0800
NmmNmNDCM 1402.0200
2
12.0600
NmmNBDM 7525.0300
Vc = V0 + ΔV A-C = 1000 N + (-200 N) = 800 N
VD = VC + ΔV C-D = 800 N + (2000 N) = 600 N
MC = M0 + ΔM A-C = -395 Nm + (180 Nm) = -215 Nm
MD = MC + ΔM C-D = -215 Nm + (+140 Nm) = -75 Nm
MB = MD +ΔM D-B = -75 Nm + (+75 Nm) = 0
1111
Using Engineering Activities To Teach Math & Science
1212
Steps for V and BM diagramsSteps for V and BM diagrams
1.Draw FBD1.Draw FBD
2.Obtain reactions:2.Obtain reactions:
M (@left support) to obtain vertical reaction at right;M (@left support) to obtain vertical reaction at right;
M (@Right support) to obtain vertical reaction at left;M (@Right support) to obtain vertical reaction at left;
Check Check Fy = 0 Fy = 0
Check Check ∑Fx = 0∑Fx = 0
3. Cut a section ;3. Cut a section ;
Obtain internal P,V,M at cut section ;Obtain internal P,V,M at cut section ;
M, M, Fy, Fy, FxFx
4. Record, draw internal P, V, M on both sides of cut sections ;4. Record, draw internal P, V, M on both sides of cut sections ;
-- magnitudemagnitude
-- unitsunits
-- direction on both sides of cutdirection on both sides of cut