Page 53 - Unistrut-Australia Catalog
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 ENGINEERING DATA [BEAM FORMULAE]
CANTILEVER BEAMS
PP
M M
M
M
M max. = Pab
Pab(a+2b) 3a(a+2b ) max. =max. at x2=7 EILa(a+2b)
P P
P
V max. = P
V max. = W Vmax. = W
a P b a b
V max. = P
ENGINEERING DATA STRUT SYSTEMS
V
PL Mmax. = PL
V
V V
V
max. = Pb(3L-b) M max. = Pb2
V V
3 max. = PL
V V
3
max. = Pb (3L-b) 6EI
M
3EI3 max. =PL
M M
8EI3 M
V
3EI max. = PL3
3EI
V
8E2I max. = WL3
V
6EI2
max. = Pb(3L-b)
6EI
BEAMS
L P
FIXED ON
27 EIL P 27 EIL
R1
16 R
V max. = 11P 1 L
8 VmaRx. = 53W
R1
R2 R2= Pa3(3L2-a) 2L2 2 R2 R21= Paba3 (3(La2+-2aL))
V
VMmax. = PPL VMmax. = WL 21
82 V 12 RV1 R2 L3
V V
8 12 L M max. = PL M max. = WL V L 2
L
P
R = 5P 1
LP 2P
R1=5P
1 16 R1=3W
a Pb
a b R1=Pb2(a+2L)
2
16 R = 3W 1 8 R1= 5P 8
2
R1 = Pb3 (a + 2L)
2
MS FIXED AT BOTH ENDS
L
L
Vmax. = P Mmax.=PL
L
a PLb
Vmax. = P Mmax. =Pb
L LL2L
V max. = P
V max. = W
b
V max. = P
M max. =
V max. = P
W L Mmax. = WL
M max. = P b V max. = P 2
3 Mmaxx.. = PPLL
max. = WL 2 3
max. = 6PEbI
max. = Pb2(3L-b)
3EI
Mmax.. = WLL 8EI
M
M MMM
M MMM
SIMPLE BEAMS
xP R=Pb
LP L P
xaPb 1
2
2 R=P R=Wx
P R = Pb 1 L ab L
48EI3 M max. = PL M
48EI
E END, SUPPORTED AT OTHER
3
2
VR Mmax.=3PL 1L
R1
1 L MVmaaxx..=31P1LP V
1 8 8
R1
2L3 2L
L
V 16
V
Mmmaax.x..at=x=3P0L.447L 3L max.atx=0.4215L Matpointofload
M
V 8
16 3 8 M max. = WL V
M at fixed end
M
max. = 0.009317 PL M 3L max. = WL 3 M max. at x = 0.447L 3 max. at x =30.4215L max. = 0.009317 PL M 8 3L max. = WL8L3 M
= R1a
M att fpixoeidndt eonfdload = Pab (a +L)
M max. = 3PL
R 3L 1 M max. = 3PL 8
8
1
2L 2 R MR2at=poinPtaof(3loLa2d- a )
16 R
Vmax. = 5W
2 R2 R2= Pa(3L2-a)
V 3L 16 R1
R1 Mmax.= WL V
M
M
384EI
max. = Pab(a+2b) 3a(a3+2b )
V max. = 11P L 8
P 1 16 R1 16 R
P
2L3
L L
Mmax.=WL
PL a
L
P L R= W P R = Pba L P R= 2 L 2 aL b R12= PLa
2L2 2xL2
V max. = P R R V max. = W L P R = PLb
LLP P R=W 1 V max.R= P R R V max. = W R1 a bR2
L R2R2L 2RRVmaRx.=Pa
2 2 1 2 2
R R 2P R= 2W2 L V max. = PLa
L M max.R= PL M max. = WL
V max. = P R L R V max. = W R = PLa M max. = P2L V M max. = W2L RV R 2
V 4 8V1L2L R L R 2 V 2 V MV max. = PPaab
V V max. = 4P3 R R V max. = 8W8 3
max. = PL max. = 5WL R R M max. = PaLab
M max. = PL3 M max. = WL3 1 2
R R max. = PL2L max. = 5W2L V V max. = PLa
48EI V 384EI V48L
M max. = 48PELI M max. =38W4ELI
M
Mmamxa.x.at=x =Paba(a+2b)
max. = PL
3 3 V max. = 5WL
MV M
max. at x =
max. at x = L a(a+2b)
V4M8
3
2L 16 R=3W 2
L L V maRx. = 151P L
1 Vmax.=5W
M max. =
V max. = W2
max. =WL 8EI
384EI3 max. = 5WL
max. at x = L a(a+2b) Pab(a+2b) 3a(a+2b )
a b 2
L
L
2 = R1a
V 8 8 3
8 MV max. = W5WL
V R
M at point3of load
max. atx=0.447L V 8 max. atx=0.4215L = R1a2L 16 Mmax.= WL V
EI 185EI
1
= RPaab2(a+L)
3L
max. at x = 0.447LEI 4 max. a1t18x5E=I0.4215L
2L
M at fixe2d end M 3 2L
M
2 BEA
max. =0.009317 PL M 4 max.= WL3 M 2L
= Pab(a+L)
3L M at fixed end EI3 185EI 2
max. =0.009317 PL M 4 max.= WL3 M 2L
EI 3L 185EI = Pab2(a+L)
LP 4 aPb2L L P P
a b
LP Vmax.=P L Vmax.=W P R1=Pb2(3a+b)
Vmax. = P Vmax. = W aL b R1 = Pb2(3a+b) 2 2 L 2 L R = Pb3(3a+b)
LP L3 LP223
2
V max. = P L V max. = W R1 R2 R1 = Pb2 (3a + b)
22abL RRL
R1 L R2 2 Mmax. = PL Mmax. = WL 3
2 2 R2 = Pa (a+3b)
L 2
8 V L 12 L R2 = Pab3 (a3a+ +3b))
3 3 R1 R2 R2=Pa(a+3b)
max. = PL V max. = WL 1 32 83 123 M = Pab
L 2
192EI 384EI MR12 = PPaab2b (a + 3b)
Mmaaxx.. = PPLL Mmaaxx.. = WLL V 1
V V L23
M M
M = Pab 2
M M 192E3I
384E3I max. = WL
M
M2 = Pa2b
max. = PL
M 192EI M
M 2
1 2 21 L 2
R - M -
Reaction Moment (Nmm)
W - V -
Total uniform load (N) Shear
- I -
DeflecMtio2n (mm)
Modulus of Elasticity (M2Pa)
M - P - R - P -
Moment (Nmm) Concentrated load (N) Reaction
Concentrated load (N)
V - L - W - L -
Shear
Length (mm)
Total uniform load (N) Length (mm)
E
I -
Modulus of Elasticity (MPa)
M - R -
Moment (Nmm) Reaction
V - W -
Shear
Total uniform load (N)
-
Modulus of Elasticity (MPa) Deflection (mm)
P - M -
Concentrated load (N) Moment (Nmm)
L - V -
Length (mm) Shear
I - E
I -
Moment of Inertia (mm4) Modulus of Elasticity (MPa)
P -
Concentrated load (N)
L -
Length (mm)
Moment of Inertia (mm4)
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51
max. = PL3
1928EI
38142EI max. = WL3
L
V 1 L 2
384EI MM2
R -
Reaction
W -
-
Deflection (mm) L2 M2 = Pab
Total uniform load (N)
L2 M1 M2M2 = Pa2b
M 1
M
max.
M
M M2 = Pa2b 1 2 L
E
L
E
Moment of Inertia (mm4) Moment of Inertia (mm )
-
MDeofmleecntitoonf (Inmemrt)ia (mm4)
aL
b
27 EIL
max. = Pab(a+2b) 3a(a+2b )
3 max. = Pab(a+2b) 3a(a+2b )
2L3
L P R1= Pb (a+2L)
C
T
E
U
R
L
T
E
S
B
4
F
2
9
1
R
O
S
I
N
A
C
E
S
R
T
A
E
Y
I
N
G
9
0
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