finite element beam in excel
TRANSCRIPT
-
8/13/2019 Finite Element Beam in Excel
1/64
-
8/13/2019 Finite Element Beam in Excel
2/64
-
8/13/2019 Finite Element Beam in Excel
3/64
-
8/13/2019 Finite Element Beam in Excel
4/64
-
8/13/2019 Finite Element Beam in Excel
5/64
-
8/13/2019 Finite Element Beam in Excel
6/64
-
8/13/2019 Finite Element Beam in Excel
7/64
-
8/13/2019 Finite Element Beam in Excel
8/64
-
8/13/2019 Finite Element Beam in Excel
9/64
Beam
Breadth (B) = 0.1473 m
Depth (D) = 0.2596 m
Top Flange (Tt) = 0.0127 m
web (tw) = 0.0072 m
Bottom Flange (Tb) = 0.0127 m
Area (A) = 0.0054277m2
Beam element length (l) = 10 m
Second moment of area about z-z axis (Iz) = 6.478E-05m
Young's modulus of Elasticity (E) = 2.05E+11N/m2
Disp
1 2 3 4 5 6
1 1.113E+08 0 0 -1.113E+08 0 0 u1 0
2 0 1.594E+05 7.968E+05 0 -1.594E+05 7.968E+05 v2 0
3 0 7.968E+05 5.312E+06 0 -7.968E+05 2.656E+06 qz1 0
4 -1.113E+08 0 0 1.113E+08 0 0 u2
0
5 0 -1.594E+05 -7.968E+05 0 1.594E+05 -7.968E+05 v2 0.02510189
6 0 7.968E+05 2.656E+06 0 -7.968E+05 5.312E+06 qz2 0.00376528
1 2 3 4 5 6
1 1.113E+08 0 0 0 0 0
2 0 1.594E+05 0 0 0 0
3 0 0 5.312E+06 0 0 0
4 0 0 0 1.113E+08 0 0
5 0 0 0 0 1.594E+05 -7.968E+05
6 0 0 0 0 -7.968E+05 5.312E+06
Force
1 2 3 4 5 6
1 8.98739E-09 0 0 0 0 0 Fx1 0
2 0 6.27547E-06 0 0 0 0 Fy1 0
3 0 0 1.88264E-07 0 0 0 Mz1 0
4 0 0 0 8.987E-09 0 0 Fx2 0
5 0 0 0 0 2.510E-05 3.765E-06 Fy2 1000
6 0 0 0 0 3.765E-06 7.531E-07 Mz2 0
Stiffness Matrix for 1 element
Apply boundary conditions (fix node 1 in x, y, z)
Invert matrix
l1
3 2 3 2
3 2 3 2
0 0 0 0 0 0 0 0 0 0
12 6 12 60 0 0 0 0 0 0
12 6 12 60 0 0 0 0 0
z z z z
y y y y
A A
l l
I I I I
l l l l
I I I I
l l l l
1u
-
8/13/2019 Finite Element Beam in Excel
10/64
2
2
3 2
3 2
0 0 0 0 0 0 0
4 6 20 0 0 0 0
4 6 20 0 0 0
0 0 0 0 0
12 60 0 0
12 60 0
0 0
40
4.
p p
y y y
z z z
z z
y y
p
y
z
GI GI
El El
I I I
l l l
I I I
l l lEA
l
I I
l l
I I
l l
GI
El
I
l
Isym
l
1
1
1
1
1
2
2
2
2
2
2
x
y
z
x
y
z
v
w
u
v
w
q
q
q
q
q
q
42m
-
8/13/2019 Finite Element Beam in Excel
11/64
Internal
Force
Fx1 0
Fy1 -1000
Mz1 -10000
Fx2
0
Fy2 1000
Mz2 0
Disp
u1 0
v2 0
qz1 0
u2 0
v2 0.02510189
qz2 0.00376528
2
1140 0 0 0 0 0 70 0 0 0 0 0 u
-
8/13/2019 Finite Element Beam in Excel
12/64
2 2
2 2
2
2
156 0 22 0 0 0 54 0 13 0
140 700 0 0 0 0 0 0
4 0 0 0 13 0 3 0
4 0 13 0 0 0 3
140 0 0 0 0 00
156 0 0 0 22
156 0 22 0
1400 0
4 0
. 4
p p
p
l l
I I
A A
l l l
l l ll
l
l
I
A
l
sym l
1
1
1
1
1
2
2
2
2
2
2
x
y
z
x
y
z
w
u
v
w
q
q
q
q
q
q
0
l
-
8/13/2019 Finite Element Beam in Excel
13/64
1
,
Px t dx
-
8/13/2019 Finite Element Beam in Excel
14/64
1
1
11
11
11
1 1
2 2
22
2
1
2
2
2
22
2
,
,
,
,
,,
,
,
,
,
,
y
y
zz
x
yy
z z
x
yy
zy
x
y
yz
z
p x t dxQ
p x t dxTm x t dx
Mp x t dx
G p x t dx Mp x t dx P
p x t dx Qp x t dx
Qm x t dx
Tp x t dx
MG p x t dx
M
ext int
f f f
-
8/13/2019 Finite Element Beam in Excel
15/64
Beam with two beam elements
Breadth (B) = 0.1473 m
Depth (D) = 0.2596 m
Top Flange (Tt) = 0.0127 m
web (tw) = 0.0072 mBottom Flange (Tb) = 0.0127 m
Area (A) = 0.0054277m2
Beam element length (l) = 5 m
Second moment of area about z-z axis (Iz) = 6.478E-05m
Young's modulus of Elasticity (E) = 2.05E+11N/m2
1. Nodal Displacement
Assembly
1 2 3 4 5 6 3
1 2.225E+08 0 0 -2.225E+08 0 0 1
2 0 1.275E+06 3.187E+06 0 -1.275E+06 3.187E+063 0 3.187E+06 1.062E+07 0 -3.187E+06 5.312E+06 2
4 -2.225E+08 0 0 2.225E+08 0 0
5 0 -1.275E+06 -3.187E+06 0 1.275E+06 -3.187E+06
6 0 3.187E+06 5.312E+06 0 -3.187E+06 1.062E+07
1 2 3 4 5 6 7 8
1 2.225E+08 0.000E+00 0.000E+00 -2.225E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 1.275E+06 3.187E+06 0.000E+00 -1.275E+06 3.187E+06 0.000E+00 0.000E+00
3 0.000E+00 3.187E+06 1.062E+07 0.000E+00 -3.187E+06 5.312E+06 0.000E+00 0.000E+00
4 -2.225E+08 0.000E+00 0.000E+00 4.451E+08 0.000E+00 0.000E+00 -2.225E+08 0.000E+00
5 0.000E+00 -1.275E+06 -3.187E+06 0.000E+00 2.550E+06 0.000E+00 0.000E+00 -1.275E+06
6 0.000E+00 3.187E+06 5.312E+06 0.000E+00 0.000E+00 2.125E+07 0.000E+00 -3.187E+06
7 0.000E+00 0.000E+00 0.000E+00 -2.225E+08 0.000E+00 0.000E+00 2.225E+08 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.275E+06 -3.187E+06 0.000E+00 1.275E+06
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 3.187E+06 5.312E+06 0.000E+00 -3.187E+06
1 2 3 4 5 6 7 8
1 2.225E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 1.275E+06 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
3 0.000E+00 0.000E+00 1.062E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
4 0.000E+00 0.000E+00 0.000E+00 4.451E+08 0.000E+00 0.000E+00 -2.225E+08 0.000E+00
5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.550E+06 0.000E+00 0.000E+00 -1.275E+06
6 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.125E+07 0.000E+00 -3.187E+06
7 0.000E+00 0.000E+00 0.000E+00 -2.225E+08 0.000E+00 0.000E+00 2.225E+08 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.275E+06 -3.187E+06 0.000E+00 1.275E+06
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 3.187E+06 5.312E+06 0.000E+00 -3.187E+06
1 2 3 4 5 6 7 8
1 4.494E-09 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
Invert stiffness matrix
Stiffness matrix of Element 1
Assembly
Apply boundary condition - Assume N1 is fixed in x, y, z (cantilever beam)
l1
-
8/13/2019 Finite Element Beam in Excel
16/64
2 0.000E+00 7.844E-07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
3 0.000E+00 0.000E+00 9.413E-08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
4 0.000E+00 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00
5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 3.138E-06 9.413E-07 0.000E+00 7.844E-06
6 0.000E+00 0.000E+00 0.000E+00 0.000E+00 9.413E-07 3.765E-07 0.000E+00 2.824E-06
7 0.000E+00 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 8.987E-09 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 7.844E-06 2.824E-06 0.000E+00 2.510E-05
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 9.413E-07 3.765E-07 0.000E+00 3.765E-06
2. Internal Forces
[u1]
1 2 3 4 5 6
2.225E+08 0 0 -2.225E+08 0 0 u1 0
0 1.275E+06 3.187E+06 0 -1.275E+06 3.187E+06 v2 0
0 3.187E+06 1.062E+07 0 -3.187E+06 5.312E+06 qz1 0
-2.225E+08 0 0 2.225E+08 0 0 u2 0
0 -1.275E+06 -3.187E+06 0 1.275E+06 -3.187E+06 v2 0.007844342
0 3.187E+06 5.312E+06 0 -3.187E+06 1.062E+07 qz2 0.002823963
[u2]
1 2 3 4 5 6
2.225E+08 0 0 -2.225E+08 0 0 u2 0
0 1.275E+06 3.187E+06 0 -1.275E+06 3.187E+06 v2 0.007844342
0 3.187E+06 1.062E+07 0 -3.187E+06 5.312E+06 qz2 0.002823963
-2.225E+08 0 0 2.225E+08 0 0 u3 0
0 -1.275E+06 -3.187E+06 0 1.275E+06 -3.187E+06 v3 0.025101894
0 3.187E+06 5.312E+06 0 -3.187E+06 1.062E+07 qz3 0.003765284
[k2] = Stiffness matrix of Element 2
[k1] = Stiffness matrix of Element 1
-
8/13/2019 Finite Element Beam in Excel
17/64
6 9
9
0.000E+00
0.000E+00
0.000E+00
0.000E+00
3.187E+06
5.312E+06
0.000E+00
-3.187E+06
1.062E+07
9
0.000E+00
0.000E+000.000E+00
0.000E+00
3.187E+06
5.312E+06
0.000E+00
-3.187E+06
1.062E+07
Force Disp
9
0.000E+00 Fx1 0 u1 0
2 3l
-
8/13/2019 Finite Element Beam in Excel
18/64
0.000E+00 Fy1 0 v2 0
0.000E+00 Mz1 0 qz1 0
0.000E+00 Fx2 0 u2 0
9.413E-07 Fy2 0 v2 0.00784434
3.765E-07 Mz2 0 qz2 0.002823960.000E+00 Fx3 0 u3 0
3.765E-06 Fy3 1000 v3 0.02510189
7.531E-07 Mz3 0 qz3 0.00376528
[k1][u1]
No. Location Length Axial Shear
fx1 (LN1) 0 Axial_LN1 0 E1_LN1 0.0 0 1000
fy1 (LN1) -1000 Shear_LN1 1 E1_LN2 5.0 0 1000
mz1 (LN1) -10000 Moment_LN1 2 E2_LN2 10.0 0 1000
fx2 (LN2) 0 Axial_LN2
fy2 (LN2) 1000 Shear_LN2
mz2 (LN2) 5000 Moment_LN2
[k2][u2]
fx2 (LN1) 0 Axial_LN1
fy2 (LN1) -1000 Shear_LN1
mz2 (LN1) -5000 Moment_LN1
fx3 (LN2) 0 Axial_LN2
fy3 (LN2) 1000 Shear_LN2
mz3 (LN2) 0 Moment_LN2
Internal forces in beam
-
8/13/2019 Finite Element Beam in Excel
19/64
-
8/13/2019 Finite Element Beam in Excel
20/64
Moment
10000
5000
0
-
8/13/2019 Finite Element Beam in Excel
21/64
Beam with two beam elements
Breadth (B) = 0.1473 m
Depth (D) = 0.2596 m
Top Flange (Tt) = 0.0127 m
web (tw) = 0.0072 m
Bottom Flange (Tb) = 0.0127 m
Area (A) = 0.0054277m2
Beam element length (l) = 2.5 m
Second moment of area about z-z axis (Iz) = 6.478E-05m
Young's modulus of Elasticity (E) = 2.05E+11N/m2
1. Nodal Displacement
Assembly
1 2 3 4 5 6 3
1 4.451E+08 0 0 -4.451E+08 0 0 1
2 0 1.020E+07 1.275E+07 0 -1.020E+07 1.275E+073 0 1.275E+07 2.125E+07 0 -1.275E+07 1.062E+07 2
4 -4.451E+08 0 0 4.451E+08 0 0
5 0 -1.020E+07 -1.275E+07 0 1.020E+07 -1.275E+07
6 0 1.275E+07 1.062E+07 0 -1.275E+07 2.125E+07
1 2 3 4 5 6 7 8
1 4.451E+08 0.000E+00 0.000E+00 -4.451E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 1.020E+07 1.275E+07 0.000E+00 -1.020E+07 1.275E+07 0.000E+00 0.000E+00
3 0.000E+00 1.275E+07 2.125E+07 0.000E+00 -1.275E+07 1.062E+07 0.000E+00 0.000E+00
4 -4.451E+08 0.000E+00 0.000E+00 8.901E+08 0.000E+00 0.000E+00 -4.451E+08 0.000E+00
5 0.000E+00 -1.020E+07 -1.275E+07 0.000E+00 2.040E+07 0.000E+00 0.000E+00 -1.020E+07
6 0.000E+00 1.275E+07 1.062E+07 0.000E+00 0.000E+00 4.249E+07 0.000E+00 -1.275E+07
7 0.000E+00 0.000E+00 0.000E+00 -4.451E+08 0.000E+00 0.000E+00 8.901E+08 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.020E+07 -1.275E+07 0.000E+00 2.040E+07
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.275E+07 1.062E+07 0.000E+00 0.000E+00
10 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -4.451E+08 0.000E+00
11 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.020E+07
12 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.275E+07
13 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
14 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
15 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
1 2 3 4 5 6 7 8
1 4.451E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 1.020E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
3 0.000E+00 0.000E+00 2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
Stiffness matrix of Element 1
Assembly
Apply boundary condition - Assume N1 is fixed in x, y, z (cantilever beam)
l
1
l
2
-
8/13/2019 Finite Element Beam in Excel
22/64
4 0.000E+00 0.000E+00 0.000E+00 8.901E+08 0.000E+00 0.000E+00 -4.451E+08 0.000E+00
5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.040E+07 0.000E+00 0.000E+00 -1.020E+07
6 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 4.249E+07 0.000E+00 -1.275E+07
7 0.000E+00 0.000E+00 0.000E+00 -4.451E+08 0.000E+00 0.000E+00 8.901E+08 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.020E+07 -1.275E+07 0.000E+00 2.040E+07
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.275E+07 1.062E+07 0.000E+00 0.000E+00
10 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -4.451E+08 0.000E+00
11 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -1.020E+07
12 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.275E+07
13 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
14 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
15 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
1 2 3 4 5 6 7 8
1 2.247E-09 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 9.805E-08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
3 0.000E+00 0.000E+00 4.707E-08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
4 0.000E+00 0.000E+00 0.000E+00 2.247E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 3.922E-07 2.353E-07 0.000E+00 9.805E-07
6 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.353E-07 1.883E-07 0.000E+00 7.060E-07
7 0.000E+00 0.000E+00 0.000E+00 2.247E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 9.805E-07 7.060E-07 0.000E+00 3.138E-06
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.353E-07 1.883E-07 0.000E+00 9.413E-07
10 0.000E+00 0.000E+00 0.000E+00 2.247E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00
11 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.569E-06 1.177E-06 0.000E+00 5.491E-06
12 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.353E-07 1.883E-07 0.000E+00 9.413E-07
13 0.000E+00 0.000E+00 0.000E+00 2.247E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00
14 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.157E-06 1.647E-06 0.000E+00 7.844E-06
15 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.353E-07 1.883E-07 0.000E+00 9.413E-07
2. Internal Forces
[u1]
1 2 3 4 5 6
4.451E+08 0 0 -4.451E+08 0 0 u1 0
0 1.020E+07 1.275E+07 0 -1.020E+07 1.275E+07 v2 0
0 1.275E+07 2.125E+07 0 -1.275E+07 1.062E+07 qz1 0
-4.451E+08 0 0 4.451E+08 0 0 u2 0
0 -1.020E+07 -1.275E+07 0 1.020E+07 -1.275E+07 v2 0.002157194
0 1.275E+07 1.062E+07 0 -1.275E+07 2.125E+07 qz2 0.001647312
[u2]
1 2 3 4 5 6
4.451E+08 0 0 -4.451E+08 0 0 u2 0
[k1] = Stiffness matrix of Element 1
[k2] = Stiffness matrix of Element 2
Invert stiffness matrix
-
8/13/2019 Finite Element Beam in Excel
23/64
0 1.020E+07 1.275E+07 0 -1.020E+07 1.275E+07 v2 0.002157194
0 1.275E+07 2.125E+07 0 -1.275E+07 1.062E+07 qz2 0.001647312
-4.451E+08 0 0 4.451E+08 0 0 u3 0
0 -1.020E+07 -1.275E+07 0 1.020E+07 -1.275E+07 v3 0.007844342
0 1.275E+07 1.062E+07 0 -1.275E+07 2.125E+07 qz3 0.002823963
[u3]
1 2 3 4 5 6
4.451E+08 0 0 -4.451E+08 0 0 u3 0
0 1.020E+07 1.275E+07 0 -1.020E+07 1.275E+07 v3 0.007844342
0 1.275E+07 2.125E+07 0 -1.275E+07 1.062E+07 qz3 0.002823963
-4.451E+08 0 0 4.451E+08 0 0 u4 0
0 -1.020E+07 -1.275E+07 0 1.020E+07 -1.275E+07 v4 0.015884793
0 1.275E+07 1.062E+07 0 -1.275E+07 2.125E+07 qz4 0.003529954
[u4]
1 2 3 4 5 6
4.451E+08 0 0 -4.451E+08 0 0 u4 0
0 1.020E+07 1.275E+07 0 -1.020E+07 1.275E+07 v4 0.015884793
0 1.275E+07 2.125E+07 0 -1.275E+07 1.062E+07 qz4 0.003529954
-4.451E+08 0 0 4.451E+08 0 0 u5 0
0 -1.020E+07 -1.275E+07 0 1.020E+07 -1.275E+07 v5 0.025101894
0 1.275E+07 1.062E+07 0 -1.275E+07 2.125E+07 qz5 0.003765284
[k3] = Stiffness matrix of Element 3
[k4] = Stiffness matrix of Element 4
-
8/13/2019 Finite Element Beam in Excel
24/64
Length Disp
0 0
10 0.02510189
Length Disp
0 0
5 0
10 0
Length Disp
6 9 12 15 0 0
2.5 0.00215719
5 0.00784434
7.5 0.01588479
3 10 0.02510189
4
9 10 11 12 13 14 15
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+001.275E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
1.062E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 -4.451E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -1.020E+07 1.275E+07 0.000E+00 0.000E+00 0.000E+00
4.249E+07 0.000E+00 -1.275E+07 1.062E+07 0.000E+00 0.000E+00 0.000E+00
0.000E+00 8.901E+08 0.000E+00 0.000E+00 -4.451E+08 0.000E+00 0.000E+00
-1.275E+07 0.000E+00 2.040E+07 0.000E+00 0.000E+00 -1.020E+07 1.275E+07
1.062E+07 0.000E+00 0.000E+00 4.249E+07 0.000E+00 -1.275E+07 1.062E+07
0.000E+00 -4.451E+08 0.000E+00 0.000E+00 4.451E+08 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -1.020E+07 -1.275E+07 0.000E+00 1.020E+07 -1.275E+07
0.000E+00 0.000E+00 1.275E+07 1.062E+07 0.000E+00 -1.275E+07 2.125E+07
9 10 11 12 13 14 15
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
Model1
Model2
Model3
43 5
ll
-
8/13/2019 Finite Element Beam in Excel
25/64
-
8/13/2019 Finite Element Beam in Excel
26/64
fy2 (LN1) -1000 Shear_LN1
mz2 (LN1) -7500 Moment_LN1
fx3 (LN2) 0 Axial_LN2
fy3 (LN2) 1000 Shear_LN2
mz3 (LN2) 5000 Moment_LN2
[k3][u3]
fx3 (LN1) 0 Axial_LN1
fy3 (LN1) -1000 Shear_LN1
mz3 (LN1) -5000 Moment_LN1
fx4 (LN2) 0 Axial_LN2
fy4 (LN2) 1000 Shear_LN2
mz4 (LN2) 2500 Moment_LN2
[k4][u4]
fx4 (LN1) 0 Axial_LN1
fy4 (LN1) -1000 Shear_LN1
mz4 (LN1) -2500 Moment_LN1
fx5 (LN2) 0 Axial_LN2
fy5 (LN2) 1000 Shear_LN2
mz5 (LN2) -4.37E-11 Moment_LN2
-
8/13/2019 Finite Element Beam in Excel
27/64
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0 2 4 6 8 10
Model1
Model2
Model3
-
8/13/2019 Finite Element Beam in Excel
28/64
Disp
u1 0v2 0
qz1 0
u2 0
v2 0.00215719
qz2 0.00164731
u3 0
v3 0.00784434
qz3 0.00282396
u4 0
v4 0.01588479
qz4 0.00352995
u5 0
v5 0.02510189
qz5 0.00376528
Shear Moment
1000 10000
1000 7500
1000 5000
1000 2500
1000 0
-
8/13/2019 Finite Element Beam in Excel
29/64
Beam with two beam elements
Breadth (B) = 0.1473 m N
Depth (D) = 0.2596 m
Top Flange (Tt) = 0.0127 m
web (tw) = 0.0072 m Analytical D
Bottom Flange (Tb) = 0.0127 m Numerical D
Area (A) = 0.00543m2
Beam element length (l) = 1.25 m
Second moment of area about z-z axis (Iz) = 6.48E-05m
Young's modulus of Elasticity (E) = 2.05E+11N/m2
Assembly
1. Nodal Displacement 3
Step1 1
1 2 3 4 5 6 2
1 8.901E+08 0 0 -8.901E+08 0 0
2 0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+073 0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07
4 -8.901E+08 0 0 8.901E+08 0 0
5 0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07
6 0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07
Step2
1 2 3 4 5 6 7 8
1 8.901E+08 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 8.159E+07 5.099E+07 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
3 0.000E+00 5.099E+07 4.249E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
4 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
5 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
6 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
7 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00
10 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
11 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07
12 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07
13 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
14 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
15 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
16 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
17 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
18 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
19 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
20 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
21 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
22 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
Stiffness matrix of Element 1
Assembly
l
1
l
2
-
8/13/2019 Finite Element Beam in Excel
30/64
23 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
24 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
25 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
26 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
27 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
Step3
1 2 3 4 5 6 7 8
1 8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 8.159E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
3 0.000E+00 0.000E+00 4.249E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
4 0.000E+00 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
6 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
7 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00
10 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
11 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07
12 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07
13 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
14 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
15 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
16 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
17 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
18 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
19 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
20 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
21 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
22 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
23 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
24 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
25 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
26 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
27 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
Step4
1 2 3 4 5 6 7 8
1 1.123E-09 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 1.226E-08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
3 0.000E+00 0.000E+00 2.353E-08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
4 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00
5 0.000E+00 0.000E+00 0.000E+00 0.000E+00 4.903E-08 5.883E-08 0.000E+00 1.226E-07
6 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.883E-08 9.413E-08 0.000E+00 1.765E-07
Apply boundary condition - Assume N1 is fixed in x, y, z (cantilever beam)
Invert stiffness matrix
-
8/13/2019 Finite Element Beam in Excel
31/64
7 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.226E-07 1.765E-07 0.000E+00 3.922E-07
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.883E-08 9.413E-08 0.000E+00 2.353E-07
10 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
11 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.961E-07 2.942E-07 0.000E+00 6.864E-07
12 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.883E-08 9.413E-08 0.000E+00 2.353E-07
13 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
14 0.000E+00 0.000E+00 0.000E+00 0.000E+00 2.696E-07 4.118E-07 0.000E+00 9.805E-07
15 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.883E-08 9.413E-08 0.000E+00 2.353E-07
16 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
17 0.000E+00 0.000E+00 0.000E+00 0.000E+00 3.432E-07 5.295E-07 0.000E+00 1.275E-06
18 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.883E-08 9.413E-08 0.000E+00 2.353E-07
19 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
20 0.000E+00 0.000E+00 0.000E+00 0.000E+00 4.167E-07 6.472E-07 0.000E+00 1.569E-06
21 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.883E-08 9.413E-08 0.000E+00 2.353E-07
22 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
23 0.000E+00 0.000E+00 0.000E+00 0.000E+00 4.903E-07 7.648E-07 0.000E+00 1.863E-06
24 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.883E-08 9.413E-08 0.000E+00 2.353E-07
25 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
26 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.638E-07 8.825E-07 0.000E+00 2.157E-06
27 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.883E-08 9.413E-08 0.000E+00 2.353E-07
2. Internal Forces
Step7 Step8 [u1]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u1 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v2 0
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz1 0
-8.901E+08 0 0 8.901E+08 0 0 u2 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v2 0.000563812
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz2 0.000882488
[u2]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u2 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v2 0.000563812
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz2 0.000882488
-8.901E+08 0 0 8.901E+08 0 0 u3 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v3 0.002157194
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz3 0.001647312
[u3]
1 2 3 4 5 6
[k1] = Stiffness matrix of Element 1
[k2] = Stiffness matrix of Element 2
[k3] = Stiffness matrix of Element 3
-
8/13/2019 Finite Element Beam in Excel
32/64
8.901E+08 0 0 -8.901E+08 0 0 u3 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v3 0.002157194
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz3 0.001647312
-8.901E+08 0 0 8.901E+08 0 0 u4 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v4 0.004633065
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz4 0.00229447
[u4]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u4 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v4 0.004633065
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz4 0.00229447
-8.901E+08 0 0 8.901E+08 0 0 u5 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v5 0.007844342
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz5 0.002823963
[u5]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u5 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v5 0.007844342
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz5 0.002823963
-8.901E+08 0 0 8.901E+08 0 0 u6 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v6 0.011643945
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz6 0.003235791
[u5]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u6 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v6 0.011643945
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz6 0.003235791
-8.901E+08 0 0 8.901E+08 0 0 u7 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v7 0.015884793
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz7 0.003529954
[u7]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u7 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v7 0.015884793
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz7 0.003529954
-8.901E+08 0 0 8.901E+08 0 0 u8 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v8 0.020419803
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz8 0.003706452
[u8]
[k6] = Stiffness matrix of Element 6
[k7] = Stiffness matrix of Element 7
[k8] = Stiffness matrix of Element 8
[k4] = Stiffness matrix of Element 4
[k5] = Stiffness matrix of Element 5
-
8/13/2019 Finite Element Beam in Excel
33/64
-
8/13/2019 Finite Element Beam in Excel
34/64
umber of Elements (N) = 8
Beam length = 10.0 m
Applied Load (F) = 1000 N
flection at free-end (d) = 0.0251019 m
flection at free-end (d) = 0.02510189 m
6 9 12 15 18 21 24 27
3
45
6
7
8
9 10 11 12 13 14 15 16 17
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
43 5
ll
6 7 8 9
llll
-
8/13/2019 Finite Element Beam in Excel
35/64
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
9 10 11 12 13 14 15 16 17
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
9 10 11 12 13 14 15 16 17
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00
5.883E-08 0.000E+00 1.961E-07 5.883E-08 0.000E+00 2.696E-07 5.883E-08 0.000E+00 3.432E-07
9.413E-08 0.000E+00 2.942E-07 9.413E-08 0.000E+00 4.118E-07 9.413E-08 0.000E+00 5.295E-07
-
8/13/2019 Finite Element Beam in Excel
36/64
-
8/13/2019 Finite Element Beam in Excel
37/64
-
8/13/2019 Finite Element Beam in Excel
38/64
fx8 (LN1) 0 Axial_LN1
fy8 (LN1) -1000 Shear_LN1
mz8 (LN1) -1250 Moment_LN1
fx9 (LN2)
0 Axial_LN2
fy9 (LN2) 1000 Shear_LN2
mz9 (LN2) 0 Moment_LN2
-
8/13/2019 Finite Element Beam in Excel
39/64
-
8/13/2019 Finite Element Beam in Excel
40/64
0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 8.901E+08 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 8.159E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 -5.099E+07
18 19 20 21 22 23 24 25 26
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 8.901E+08 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 8.159E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 -5.099E+07
18 19 20 21 22 23 24 25 26
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00
5.883E-08 0.000E+00 4.167E-07 5.883E-08 0.000E+00 4.903E-07 5.883E-08 0.000E+00 5.638E-07
9.413E-08 0.000E+00 6.472E-07 9.413E-08 0.000E+00 7.648E-07 9.413E-08 0.000E+00 8.825E-07
-
8/13/2019 Finite Element Beam in Excel
41/64
0.000E+00 2.247E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
2.353E-07 0.000E+00 1.569E-06 2.353E-07 0.000E+00 1.863E-06 2.353E-07 0.000E+00 2.157E-06
1.883E-07 0.000E+00 1.177E-06 1.883E-07 0.000E+00 1.412E-06 1.883E-07 0.000E+00 1.647E-06
0.000E+00 3.370E-09 0.000E+00 0.000E+00 3.370E-09 0.000E+00 0.000E+00 3.370E-09 0.000E+00
5.295E-07 0.000E+00 3.309E-06 5.295E-07 0.000E+00 3.971E-06 5.295E-07 0.000E+00 4.633E-06
2.824E-07 0.000E+00 1.588E-06 2.824E-07 0.000E+00 1.941E-06 2.824E-07 0.000E+00 2.294E-06
0.000E+00 4.494E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00
9.413E-07 0.000E+00 5.491E-06 9.413E-07 0.000E+00 6.668E-06 9.413E-07 0.000E+00 7.844E-06
3.765E-07 0.000E+00 1.883E-06 3.765E-07 0.000E+00 2.353E-06 3.765E-07 0.000E+00 2.824E-06
0.000E+00 5.617E-09 0.000E+00 0.000E+00 5.617E-09 0.000E+00 0.000E+00 5.617E-09 0.000E+00
1.471E-06 0.000E+00 7.967E-06 1.471E-06 0.000E+00 9.805E-06 1.471E-06 0.000E+00 1.164E-05
4.707E-07 0.000E+00 2.059E-06 4.707E-07 0.000E+00 2.647E-06 4.707E-07 0.000E+00 3.236E-06
0.000E+00 6.741E-09 0.000E+00 0.000E+00 6.741E-09 0.000E+00 0.000E+00 6.741E-09 0.000E+00
2.059E-06 0.000E+00 1.059E-05 2.118E-06 0.000E+00 1.324E-05 2.118E-06 0.000E+00 1.588E-05
4.707E-07 0.000E+00 2.118E-06 5.648E-07 0.000E+00 2.824E-06 5.648E-07 0.000E+00 3.530E-06
0.000E+00 6.741E-09 0.000E+00 0.000E+00 7.864E-09 0.000E+00 0.000E+00 7.864E-09 0.000E+00
2.647E-06 0.000E+00 1.324E-05 2.824E-06 0.000E+00 1.682E-05 2.883E-06 0.000E+00 2.042E-05
4.707E-07 0.000E+00 2.118E-06 5.648E-07 0.000E+00 2.883E-06 6.589E-07 0.000E+00 3.706E-06
0.000E+00 6.741E-09 0.000E+00 0.000E+00 7.864E-09 0.000E+00 0.000E+00 8.987E-09 0.000E+00
3.236E-06 0.000E+00 1.588E-05 3.530E-06 0.000E+00 2.042E-05 3.706E-06 0.000E+00 2.510E-05
4.707E-07 0.000E+00 2.118E-06 5.648E-07 0.000E+00 2.883E-06 6.589E-07 0.000E+00 3.765E-06
Shear Moment
1000 10000
1000 8750
1000 7500
1000 6250
1000 5000
1000 3750
1000 2500
1000 1250
1000 0
-
8/13/2019 Finite Element Beam in Excel
42/64
-
8/13/2019 Finite Element Beam in Excel
43/64
-
8/13/2019 Finite Element Beam in Excel
44/64
27
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
4 6 8 10
Model 1
Model 2
Model 3
Model 4
-
8/13/2019 Finite Element Beam in Excel
45/64
5.099E+07
2.125E+07
0.000E+00
-5.099E+07
4.249E+07
27
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
5.099E+07
2.125E+07
0.000E+00
-5.099E+07
4.249E+07
Step5 Force Step6 Disp
27
0.000E+00 Fx1 0 u1 0
0.000E+00 Fy1 0 v2 0
0.000E+00 Mz1 0 qz1 0
0.000E+00 Fx2 0 u2 0
5.883E-08 Fy2 0 v2 0.00056381
9.413E-08 Mz2 0 qz2 0.00088249
-
8/13/2019 Finite Element Beam in Excel
46/64
0.000E+00 Fx3 0 u3 0
2.353E-07 Fy3 0 v3 0.00215719
1.883E-07 Mz3 0 qz3 0.00164731
0.000E+00 Fx4 0 u4 0
5.295E-07 Fy4 0 v4 0.00463306
2.824E-07 Mz4 0 qz4 0.00229447
0.000E+00 Fx5 0 u5 0
9.413E-07 Fy5 0 v5 0.00784434
3.765E-07 Mz5 0 qz5 0.00282396
0.000E+00 Fx6 0 u6 0
1.471E-06 Fy6 0 v6 0.01164395
4.707E-07 Mz6 0 qz6 0.00323579
0.000E+00 Fx7 0 u7 0
2.118E-06 Fy7 0 v7 0.01588479
5.648E-07 Mz7 0 qz7 0.00352995
0.000E+00 Fx8 0 u8 02.883E-06 Fy8 0 v8 0.0204198
6.589E-07 Mz8 0 qz8 0.00370645
0.000E+00 Fx9 0 u9 0
3.765E-06 Fy9 1000 v9 0.02510189
7.531E-07 Mz9 0 qz9 0.00376528
-
8/13/2019 Finite Element Beam in Excel
47/64
Beam with two beam elements
Breadth (B) = 0.1473 m Nu
Depth (D) = 0.2596 m
Top Flange (Tt) = 0.0127 m
web (tw) = 0.0072 m Analytical Defl
Bottom Flange (Tb) = 0.0127 m Numerical Defl
Area (A) = 0.01m2
Beam element length (l) = 1.25 m
Second moment of area about z-z axis (Iz) = 6.48E-05m
Young's modulus of Elasticity (E) = 2.05E+11N/m2
Assembly
3
1
Step1
1 2 3 4 5 6 2
1 8.901E+08 0 0 -8.901E+08 0 0
2 0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07
3 0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+074 -8.901E+08 0 0 8.901E+08 0 0
5 0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07
6 0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07
Step2
1 2 3 4 5 6 7 8
1 8.901E+08 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2 0.000E+00 8.159E+07 5.099E+07 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
3 0.000E+00 5.099E+07 4.249E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
4 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
5 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
6 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
7 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00
8 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08
9 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00
10 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
11 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07
12 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07
13 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
14 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
15 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
16 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
17 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
18 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
19 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
20 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
21 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
22 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
Stiffness matrix of Element 1
Assembly
l1
l
2
-
8/13/2019 Finite Element Beam in Excel
48/64
-
8/13/2019 Finite Element Beam in Excel
49/64
7 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
8 0.000E+00 0.000E+00 4.118E-07 0.000E+00 4.964E-07 3.677E-07 0.000E+00 8.825E-07
9 0.000E+00 0.000E+00 8.629E-08 0.000E+00 1.103E-07 9.217E-08 0.000E+00 2.353E-07
10 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
11 0.000E+00 0.000E+00 4.780E-07 0.000E+00 5.822E-07 4.412E-07 0.000E+00 1.072E-06
12 0.000E+00 0.000E+00 2.157E-08 0.000E+00 2.942E-08 2.746E-08 0.000E+00 7.354E-08
13 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
14 0.000E+00 0.000E+00 4.707E-07 0.000E+00 5.761E-07 4.412E-07 0.000E+00 1.079E-06
15 0.000E+00 0.000E+00 -3.138E-08 0.000E+00 -3.677E-08 -2.549E-08 0.000E+00 -5.883E-08
16 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
17 0.000E+00 0.000E+00 4.045E-07 0.000E+00 4.964E-07 3.824E-07 0.000E+00 9.376E-07
18 0.000E+00 0.000E+00 -7.256E-08 0.000E+00 -8.825E-08 -6.668E-08 0.000E+00 -1.618E-07
19 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
20 0.000E+00 0.000E+00 2.942E-07 0.000E+00 3.616E-07 2.795E-07 0.000E+00 6.864E-07
21 0.000E+00 0.000E+00 -1.020E-07 0.000E+00 -1.250E-07 -9.609E-08 0.000E+00 -2.353E-07
22 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
23 0.000E+00 0.000E+00 1.544E-07 0.000E+00 1.900E-07 1.471E-07 0.000E+00 3.616E-07
24 0.000E+00 0.000E+00 -1.196E-07 0.000E+00 -1.471E-07 -1.137E-07 0.000E+00 -2.795E-07
25 0.000E+00 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
26 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
27 0.000E+00 0.000E+00 -1.255E-07 0.000E+00 -1.544E-07 -1.196E-07 0.000E+00 -2.942E-07
2. Internal Forces
Step7 Step8 [u1]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u1 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v2 0
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz1 -0.000423104
-8.901E+08 0 0 8.901E+08 0 0 u2 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v2 -0.000518462
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz2 -0.0003981
[u2]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u2 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v2 -0.000518462
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz2 -0.0003981
-8.901E+08 0 0 8.901E+08 0 0 u3 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v3 -0.000974414
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz3 -0.000323089
[u3]
1 2 3 4 5 6
[k1] = Stiffness matrix of Element 1
[k2] = Stiffness matrix of Element 2
[k3] = Stiffness matrix of Element 3
-
8/13/2019 Finite Element Beam in Excel
50/64
8.901E+08 0 0 -8.901E+08 0 0 u3 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v3 -0.000974414
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz3 -0.000323089
-8.901E+08 0 0 8.901E+08 0 0 u4 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v4 -0.001305348
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz4 -0.00019807
[u4]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u4 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v4 -0.001305348
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz4 -0.00019807
-8.901E+08 0 0 8.901E+08 0 0 u5 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v5 -0.001465911
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz5 -4.06925E-05
[u5]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u5 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v5 -0.001465911
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz5 -4.06925E-05
-8.901E+08 0 0 8.901E+08 0 0 u6 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v6 -0.001386242
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz6 0.000166692
[u5]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u6 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v6 -0.001386242
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz6 0.000166692
-8.901E+08 0 0 8.901E+08 0 0 u7 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v7 -0.001065115
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz7 0.000335836
[u7]
1 2 3 4 5 6
8.901E+08 0 0 -8.901E+08 0 0 u7 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v7 -0.001065115
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz7 0.000335836
-8.901E+08 0 0 8.901E+08 0 0 u8 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v8 -0.000574843
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz8 0.000437322
[u8]
1 2 3 4 5 6
[k4] = Stiffness matrix of Element 4
[k5] = Stiffness matrix of Element 5
[k6] = Stiffness matrix of Element 6
[k7] = Stiffness matrix of Element 7
[k8] = Stiffness matrix of Element 8
-
8/13/2019 Finite Element Beam in Excel
51/64
8.901E+08 0 0 -8.901E+08 0 0 u8 0
0 8.159E+07 5.099E+07 0 -8.159E+07 5.099E+07 v8 -0.000574843
0 5.099E+07 4.249E+07 0 -5.099E+07 2.125E+07 qz8 0.000437322
-8.901E+08 0 0 8.901E+08 0 0 u9 0
0 -8.159E+07 -5.099E+07 0 8.159E+07 -5.099E+07 v9 0
0 5.099E+07 2.125E+07 0 -5.099E+07 4.249E+07 qz9 0.000471151
3. Interrogating Internal forces
Step12 x 0.000 LN2- x 1.000
N1" G1" N2" G2" Elem1 Elem2 Elem3 Elem4
0.000E+00 -5.185E-04 -9.744E-04 -1.305E-03
-3.840 -3.200 3.840 -1.600 -4.231E-04 -3.981E-04 -3.231E-04 -1.981E-04
-5.185E-04 -9.744E-04 -1.305E-03 -1.466E-03
3.840 1.600 -3.840 3.200 -3.981E-04 -3.231E-04 -1.981E-04 -4.069E-05
0 531 1062 1094
531 1062 1594 2250
Step13 x 0.000 LN2- x 1.000
N1" G1" N2" G2" Elem1 Elem2 Elem3 Elem4
0.000E+00 -5.185E-04 -9.744E-04 -1.305E-03
6.144 3.840 -6.144 3.840 -4.231E-04 -3.981E-04 -3.231E-04 -1.981E-04
-5.185E-04 -9.744E-04 -1.305E-03 -1.466E-03
-3.981E-04 -3.231E-04 -1.981E-04 -4.069E-05
-425.0 -425.0 -425.0 -925.0
-425.0 -425.0 -425.0 -925.0
Local Node 1
Local Node 2
Second derivates of shape functions
Local Node 1 & 2
Shear Force in element at LN1
Shear Force in element at LN2
Nodal Displ
Bending Moment in element at LN1
Bending Moment in element at LN2
Second derivates of shape functions Nodal Displ
-
8/13/2019 Finite Element Beam in Excel
52/64
ber of Elements (N) = 8
Beam length = 10.0 m
Applied Load (F) = 1000 N
ction at mid-span (d) = 0.0015689 m PL only at mid-span
ction at mid-span (d) = -0.00146591 m
6 9 12 15 18 21 24 27
3
4
56
7
8
9 10 11 12 13 14 15 16 17
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
43 5
ll
6 7 8 9
llll
-
8/13/2019 Finite Element Beam in Excel
53/64
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
9 10 11 12 13 14 15 16 17
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
9 10 11 12 13 14 15 16 17
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
8.629E-08 0.000E+00 4.780E-07 2.157E-08 0.000E+00 4.707E-07 -3.138E-08 0.000E+00 4.045E-07
0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00
1.103E-07 0.000E+00 5.822E-07 2.942E-08 0.000E+00 5.761E-07 -3.677E-08 0.000E+00 4.964E-07
9.217E-08 0.000E+00 4.412E-07 2.746E-08 0.000E+00 4.412E-07 -2.549E-08 0.000E+00 3.824E-07
-
8/13/2019 Finite Element Beam in Excel
54/64
0.000E+00 2.247E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
2.353E-07 0.000E+00 1.072E-06 7.354E-08 0.000E+00 1.079E-06 -5.883E-08 0.000E+00 9.376E-07
1.098E-07 0.000E+00 3.309E-07 4.510E-08 0.000E+00 3.530E-07 -7.844E-09 0.000E+00 3.162E-07
0.000E+00 3.370E-09 0.000E+00 0.000E+00 3.370E-09 0.000E+00 0.000E+00 3.370E-09 0.000E+00
3.309E-07 0.000E+00 1.379E-06 1.471E-07 0.000E+00 1.434E-06 -5.148E-08 0.000E+00 1.269E-06
4.510E-08 0.000E+00 1.471E-07 7.452E-08 0.000E+00 2.059E-07 2.157E-08 0.000E+00 2.059E-07
0.000E+00 3.370E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00
3.530E-07 0.000E+00 1.434E-06 2.059E-07 0.000E+00 1.569E-06 7.211E-22 0.000E+00 1.434E-06
-7.844E-09 0.000E+00 -5.148E-08 2.157E-08 0.000E+00 7.306E-22 6.275E-08 0.000E+00 5.148E-08
0.000E+00 3.370E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 5.617E-09 0.000E+00
3.162E-07 0.000E+00 1.269E-06 2.059E-07 0.000E+00 1.434E-06 5.148E-08 0.000E+00 1.379E-06
-4.903E-08 0.000E+00 -2.059E-07 -1.961E-08 0.000E+00 -2.059E-07 2.157E-08 0.000E+00 -1.471E-07
0.000E+00 3.370E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 5.617E-09 0.000E+00
2.353E-07 0.000E+00 9.376E-07 1.618E-07 0.000E+00 1.079E-06 5.883E-08 0.000E+00 1.072E-06
-7.844E-08 0.000E+00 -3.162E-07 -4.903E-08 0.000E+00 -3.530E-07 -7.844E-09 0.000E+00 -3.309E-07
0.000E+00 3.370E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 5.617E-09 0.000E+00
1.250E-07 0.000E+00 4.964E-07 8.825E-08 0.000E+00 5.761E-07 3.677E-08 0.000E+00 5.822E-07
-9.609E-08 0.000E+00 -3.824E-07 -6.668E-08 0.000E+00 -4.412E-07 -2.549E-08 0.000E+00 -4.412E-07
0.000E+00 3.370E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 5.617E-09 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-1.020E-07 0.000E+00 -4.045E-07 -7.256E-08 0.000E+00 -4.707E-07 -3.138E-08 0.000E+00 -4.780E-07
Step9 [k1][u1] Step10
No. Location Length Axialfx1 (LN1) 0 Axial_LN1 0 E1_LN1 0.00 0
fy1 (LN1) 425 Shear_LN1 1 E1_LN2 1.25 0
mz1 (LN1) 5.45697E-12 Moment_LN1 2 E2_LN2 2.50 0
fx2 (LN2) 0 Axial_LN2 3 E3_LN2 3.75 0
fy2 (LN2) -425 Shear_LN2 4 E4_LN2 5.00 0
mz2 (LN2) 531.25 Moment_LN2 5 E5_LN2 6.25 0
6 E6_LN2 7.50 0
[k2][u2] 7 E7_LN2 8.75 0
8 E8_LN2 10.00 0
fx2 (LN1) 0 Axial_LN1
fy2 (LN1) 425 Shear_LN1
mz2 (LN1) -531.25 Moment_LN1
fx3 (LN2) 0 Axial_LN2
fy3 (LN2) -425 Shear_LN2
mz3 (LN2) 1062.5 Moment_LN2
[k3][u3]
Internal forces in beam [ku]
1000
1500
2000
2500
-
8/13/2019 Finite Element Beam in Excel
55/64
fx3 (LN1) 0 Axial_LN1
fy3 (LN1) 425 Shear_LN1
mz3 (LN1) -1062.5 Moment_LN1
fx4 (LN2) 0 Axial_LN2
fy4 (LN2) -425 Shear_LN2mz4 (LN2) 1594 Moment_LN2
[k4][u4]
fx4 (LN1) 0 Axial_LN1
fy4 (LN1) 925 Shear_LN1
mz4 (LN1) -1093.75 Moment_LN1
fx5 (LN2) 0 Axial_LN2
fy5 (LN2) -925 Shear_LN2
mz5 (LN2) 2250 Moment_LN2
[k5][u5]
fx5 (LN1) 0 Axial_LN1
fy5 (LN1) -75 Shear_LN1
mz5 (LN1) -2250 Moment_LN1
fx6 (LN2) 0 Axial_LN2
fy6 (LN2) 75 Shear_LN2
mz6 (LN2) 2156 Moment_LN2
[k6][u6]
fx6 (LN1) 0 Axial_LN1
fy6 (LN1) -575 Shear_LN1
mz6 (LN1) -2156.25 Moment_LN1
fx7 (LN2) 0 Axial_LN2
fy7 (LN2) 575 Shear_LN2
mz7 (LN2) 1438 Moment_LN2
[k7][u7]
fx7 (LN1) 0 Axial_LN1
fy7 (LN1) -575 Shear_LN1
mz7 (LN1) -1437.5 Moment_LN1
fx8 (LN2) 0 Axial_LN2
fy8 (LN2) 575 Shear_LN2
mz8 (LN2) 719 Moment_LN2
[k8][u8]
-500
0
500
0.00 2.00 4.00 6.00
-
8/13/2019 Finite Element Beam in Excel
56/64
fx8 (LN1) 0 Axial_LN1
fy8 (LN1) -575 Shear_LN1
mz8 (LN1) -718.75 Moment_LN1
fx9 (LN2) 0 Axial_LN2
fy9 (LN2) 575 Shear_LN2
mz9 (LN2) 0 Moment_LN2
For comparison purposes
Shear Moment Shear
E1_LN1 -425 0 -425
E1_LN2 -425 531 -425
Elem5 Elem6 Elem7 Elem8 E2_LN2 -425 1062 -425
-1.466E-03 -1.386E-03 -1.065E-03 -5.748E-04 E3_LN2 -425 1594 -925
-4.069E-05 1.667E-04 3.358E-04 4.373E-04 E4_LN2 -925 2250 75
-1.386E-03 -1.065E-03 -5.748E-04 0.000E+00 E5_LN2 75 2156 575
1.667E-04 3.358E-04 4.373E-04 4.712E-04 E6_LN2 575 1438 575
2250 2156 1437 719 E7_LN2 575 719 575
2156 1438 719 0 E8_LN2 575 0 575
Elem5 Elem6 Elem7 Elem8
-1.466E-03 -1.386E-03 -1.065E-03 -5.748E-04
-4.069E-05 1.667E-04 3.358E-04 4.373E-04
-1.386E-03 -1.065E-03 -5.748E-04 0.000E+00
1.667E-04 3.358E-04 4.373E-04 4.712E-04
75.0 575.0 575.0 575.0
75.0 575.0 575.0 575.0
acements
[k][u]- f
acements
[k][u]= fintLocation
-
8/13/2019 Finite Element Beam in Excel
57/64
Length u v q
0.00 0 0 -0.0004231
1.25 0 -0.00051846 -0.0003981
2.50 0 -0.00097441 -0.00032309
3.75 0 -0.00130535 -0.00019807
5.00 0 -0.00146591 -4.0693E-05
6.25 0 -0.00138624 0.00016669
7.50 0 -0.00106511 0.00033584
8.75 0 -0.00057484 0.00043732
10.00 0 0 0.00047115
18 19 20 21 22 23 24 25 26
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
Displacements (in metres)
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.00 2.00 4.00
u
-
8/13/2019 Finite Element Beam in Excel
58/64
0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07
0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 8.901E+08 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 8.159E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 -5.099E+07
18 19 20 21 22 23 24 25 26
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 -8.159E+07 5.099E+07 0.000E+00 0.000E+00
2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 -5.099E+07 2.125E+07 0.000E+00 0.000E+00
0.000E+00 -8.901E+08 0.000E+00 0.000E+00 1.780E+09 0.000E+00 0.000E+00 -8.901E+08 0.000E+00
0.000E+00 0.000E+00 -8.159E+07 -5.099E+07 0.000E+00 1.632E+08 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00 8.499E+07 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 -8.901E+08 0.000E+00 0.000E+00 8.901E+08 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 8.159E+07
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 5.099E+07 2.125E+07 0.000E+00 0.000E+00
18 19 20 21 22 23 24 25 26
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
-7.256E-08 0.000E+00 2.942E-07 -1.020E-07 0.000E+00 1.544E-07 -1.196E-07 0.000E+00 0.000E+00
0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00 0.000E+00 1.123E-09 0.000E+00
-8.825E-08 0.000E+00 3.616E-07 -1.250E-07 0.000E+00 1.900E-07 -1.471E-07 0.000E+00 0.000E+00
-6.668E-08 0.000E+00 2.795E-07 -9.609E-08 0.000E+00 1.471E-07 -1.137E-07 0.000E+00 0.000E+00
-
8/13/2019 Finite Element Beam in Excel
59/64
0.000E+00 2.247E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00 0.000E+00 2.247E-09 0.000E+00
-1.618E-07 0.000E+00 6.864E-07 -2.353E-07 0.000E+00 3.616E-07 -2.795E-07 0.000E+00 0.000E+00
-4.903E-08 0.000E+00 2.353E-07 -7.844E-08 0.000E+00 1.250E-07 -9.609E-08 0.000E+00 0.000E+00
0.000E+00 3.370E-09 0.000E+00 0.000E+00 3.370E-09 0.000E+00 0.000E+00 3.370E-09 0.000E+00
-2.059E-07 0.000E+00 9.376E-07 -3.162E-07 0.000E+00 4.964E-07 -3.824E-07 0.000E+00 0.000E+00
-1.961E-08 0.000E+00 1.618E-07 -4.903E-08 0.000E+00 8.825E-08 -6.668E-08 0.000E+00 0.000E+00
0.000E+00 4.494E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00 0.000E+00 4.494E-09 0.000E+00
-2.059E-07 0.000E+00 1.079E-06 -3.530E-07 0.000E+00 5.761E-07 -4.412E-07 0.000E+00 0.000E+00
2.157E-08 0.000E+00 5.883E-08 -7.844E-09 0.000E+00 3.677E-08 -2.549E-08 0.000E+00 0.000E+00
0.000E+00 5.617E-09 0.000E+00 0.000E+00 5.617E-09 0.000E+00 0.000E+00 5.617E-09 0.000E+00
-1.471E-07 0.000E+00 1.072E-06 -3.309E-07 0.000E+00 5.822E-07 -4.412E-07 0.000E+00 0.000E+00
7.452E-08 0.000E+00 -7.354E-08 4.510E-08 0.000E+00 -2.942E-08 2.746E-08 0.000E+00 0.000E+00
0.000E+00 6.741E-09 0.000E+00 0.000E+00 6.741E-09 0.000E+00 0.000E+00 6.741E-09 0.000E+00
-7.354E-08 0.000E+00 8.825E-07 -2.353E-07 0.000E+00 4.964E-07 -3.677E-07 0.000E+00 0.000E+00
4.510E-08 0.000E+00 -2.353E-07 1.098E-07 0.000E+00 -1.103E-07 9.217E-08 0.000E+00 0.000E+00
0.000E+00 6.741E-09 0.000E+00 0.000E+00 7.864E-09 0.000E+00 0.000E+00 7.864E-09 0.000E+00
-2.942E-08 0.000E+00 4.964E-07 -1.103E-07 0.000E+00 3.003E-07 -2.059E-07 0.000E+00 0.000E+00
2.746E-08 0.000E+00 -3.677E-07 9.217E-08 0.000E+00 -2.059E-07 1.687E-07 0.000E+00 0.000E+00
0.000E+00 6.741E-09 0.000E+00 0.000E+00 7.864E-09 0.000E+00 0.000E+00 8.987E-09 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.226E-08
2.157E-08 0.000E+00 -4.118E-07 8.629E-08 0.000E+00 -2.574E-07 1.628E-07 0.000E+00 0.000E+00
Step11
Shear Moment Shear Moment
-425 0 -425 0
-425 531 -425 531
-425 1062 -425 1062
-425 1594 -925 1094
-925 2250 75 2250
75 2156 575 2156
575 1438 575 1438
575 719 575 719
575 0 575 0
[k][u]- fext= fint
BM
-200
0
200
400
600
800
0.00 2.00 4.00 6.00 8.00 10.00
-
8/13/2019 Finite Element Beam in Excel
60/64
8.00 10.00
-1000
-800
-600
-400
SF
-
8/13/2019 Finite Element Beam in Excel
61/64
Moment
0
531
1062
10942250
2156
1438
719
0
ext= fint
-
8/13/2019 Finite Element Beam in Excel
62/64
27
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
6.00 8.00 10.00
v theta
-
8/13/2019 Finite Element Beam in Excel
63/64
5.099E+07
2.125E+07
0.000E+00
-5.099E+07
4.249E+07
27
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
0.000E+00
5.099E+07
2.125E+07
0.000E+00
0.000E+00
4.249E+07
Step5 Force Step6 Disp
27
0.000E+00 Fx1 0 u1 0
0.000E+00 Fy1 0 v2 0
-1.255E-07 Mz1 0 qz1 -0.0004231
0.000E+00 Fx2 0 u2 0
-1.544E-07 Fy2 0 v2 -0.00051846
-1.196E-07 Mz2 0 qz2 -0.0003981
-
8/13/2019 Finite Element Beam in Excel
64/64
0.000E+00 Fx3 0 u3 0
-2.942E-07 Fy3 0 v3 -0.00097441
-1.020E-07 Mz3 0 qz3 -0.00032309
0.000E+00 Fx4 0 u4 0
-4.045E-07 Fy4 500 v4 -0.00130535
-7.256E-08 Mz4 500 qz4 -0.00019807
0.000E+00 Fx5 0 u5 0
-4.707E-07 Fy5 -1000 v5 -0.00146591
-3.138E-08 Mz5 0 qz5 -4.0693E-05
0.000E+00 Fx6 0 u6 0
-4.780E-07 Fy6 -500 v6 -0.00138624
2.157E-08 Mz6 0 qz6 0.00016669
0.000E+00 Fx7 0 u7 0
-4.118E-07 Fy7 0 v7 -0.00106511
8.629E-08 Mz7 0 qz7 0.00033584
0.000E+00 Fx8 0 u8 0-2.574E-07 Fy8 0 v8 -0.00057484
1.628E-07 Mz8 0 qz8 0.00043732
0.000E+00 Fx9 0 u9 0
0.000E+00 Fy9 0 v9 0
2.510E-07 Mz9 0 qz9 0.00047115