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Beam Values
Length, L (mm) 100
Width, W (mm) 25
Height, H (mm) 6
Length increment, Linc (mm) 1
Modulus of elasticity, E (N/mm^2) 200000
Moment of inertia, I (mm^4) 450
Distance farthest fiber to nuetral axis, cc (mm) 3
Loading
Point load, F (N) 10
Location of point load, af (mm) 50
Distributed load amplitude, wa, (N/mm) 1
Distributed load amplitude, wL, (N/mm) 1
Starting point of load, aw (mm) 50
Total distributed load (N) 50
Moment load, M (N-mm) 10
Location of moment load, am (mm) 25
Maximum deflection (microns) -9.643
Maximum slope (milli radians) -0.273
Reactions at beam ends
RA, Ra (N) 17.40
RB, Rb (N) 42.60
MA, Ma (N) 0
MB, Mb (N-mm) 0
qA, ta (radians) -0.00027
qB, tb (radians) 0.000332
dA, da (microns) 0
dB, db (microns) 0
Equations
Enters numbe
Beam
To determine deflection of a sim
By Alex Slocum, las
M
wa
aw
af
am
A
x
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0
2
2
2
3
3
2
2 2 6
6 6 24
A af w
a wA f
f aAA
f aAA
V F x a x awR
x awM x F x aR
F x a xwxR
EI EI E
F x a xwxRx
EI EI
q q
d q
2
22
2
2
6
2
6 24
1
6 24
f L awA
f f f wA
f
B a w
F L a L a w wR L L
Fa L a L a L a
EIL EIL
aFa Law L
EIL EIL
q
q
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Schematic
Instructions
Enter total length of beam in mm
Enter width of beam in mm
Enter height of beam in mm
Enter length increment to be used in finite difference calculation
Enter elastic modulus in N/mm^2
=1/12*W*H^3
= H/2
See schematic for definitions of loads and positions
Enter amplitude of the point load, in N
Enter location of the point load, in mm
Enter amplitude of the distributed load near the cantilever end, in N/mm
Enter amplitude of the distributed load at the clamped end, in N/mm
Enter location where the distributed load starts, in mm
Resulted total distributed load
Enter amplitude of the applied moment, in N*mm
Enter location of the moment load, in mm
Return maximum deflection along the beam in microns
Return maximum slope along the beam in milli radians
Reaction force at A
Reaction force at B
Reaction moment at A
Reaction moment at B
Rotation at A
Rotation at B
Deflection at A
Deflection at B
rs in BOLD, Results in RED
simply_supported.xls
ply supported beam under superimposed loads
y Alex Slocum
modified 06/11/04 by Xue'en Yang
FwL
B
L
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3
0
3 4
4 5 2
2
6
24
120 2
L a w
w
L a w
m
w
L aw w m
w
L aw w m
w
x aw
L a
x aw wM x a
L a
a x a M x aw w
EI L a EI
a x a M x aw w
I EI L a
EI
22 2 2
22
2
22
2
2 3
6 3 6 37 22
15 6
L af w wB L a
L a w w m m
a w w
L a
Fa L a L aM w w Mw wRL L L L
a L a M a L aw w L La L aw L
EIL
Lw w
2 22 29 3 3815 6
w w w ma a L a M aL L
EIL
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-12.0
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
0 50 100 150
Deflection(mcrons)
Distance from left end of beam (mm)
Deflection
-100
0
100
200
300
400
500
600
700
800
900
1000
0 50 100 150
Moment(N-mm)
Distance from left end of beam (mm)
Moment
10
20
30
Transverse Shear
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-0.400
-0.300
-0.200
-0.100
0.000
0.100
0.200
0.300
0.400
0 50 100 150
Slope(milliradians)
Distance from left end of beam (mm)
Slope
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0 50 100 150
Stress(Pa)
Distance from left end of beam (mm)
Stress
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Distance along beam, x Shear (N) Moment (N-mm) Stress (Pa)
0 17 0 0.0
1 17 17 0.1
2 17 35 0.2
3 17 52 0.3
4 17 70 0.5
5 17 87 0.66 17 104 0.7
7 17 122 0.8
8 17 139 0.9
9 17 157 1.0
10 17 174 1.2
11 17 191 1.3
12 17 209 1.4
13 17 226 1.5
14 17 244 1.6
15 17 261 1.7
16 17 278 1.9
17 17 296 2.018 17 313 2.1
19 17 331 2.2
20 17 348 2.3
21 17 365 2.4
22 17 383 2.6
23 17 400 2.7
24 17 418 2.8
25 17 435 2.9
26 17 462 3.1
27 17 480 3.2
28 17 497 3.3
29 17 515 3.4
30 17 532 3.5
31 17 549 3.7
32 17 567 3.8
33 17 584 3.9
34 17 602 4.0
35 17 619 4.1
36 17 636 4.2
37 17 654 4.4
38 17 671 4.5
39 17 689 4.6
40 17 706 4.7
41 17 723 4.8
42 17 741 4.943 17 758 5.1
44 17 776 5.2
45 17 793 5.3
46 17 810 5.4
47 17 828 5.5
48 17 845 5.6
49 17 863 5.8
50 17 880 5.9
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51 6 887 5.9
52 5 893 6.0
53 4 898 6.0
54 3 902 6.0
55 2 905 6.0
56 1 906 6.0
57 0 907 6.058 -1 907 6.0
59 -2 906 6.0
60 -3 904 6.0
61 -4 901 6.0
62 -5 897 6.0
63 -6 892 5.9
64 -7 886 5.9
65 -8 879 5.9
66 -9 870 5.8
67 -10 861 5.7
68 -11 851 5.7
69 -12 840 5.670 -13 828 5.5
71 -14 815 5.4
72 -15 801 5.3
73 -16 786 5.2
74 -17 770 5.1
75 -18 753 5.0
76 -19 734 4.9
77 -20 715 4.8
78 -21 695 4.6
79 -22 674 4.5
80 -23 652 4.3
81 -24 629 4.2
82 -25 605 4.0
83 -26 580 3.9
84 -27 554 3.7
85 -28 527 3.5
86 -29 498 3.3
87 -30 469 3.1
88 -31 439 2.9
89 -32 408 2.7
90 -33 376 2.5
91 -34 343 2.3
92 -35 309 2.1
93 -36 274 1.8
94 -37 238 1.695 -38 201 1.3
96 -39 162 1.1
97 -40 123 0.8
98 -41 83 0.6
99 -42 42 0.3
100 -43 0 0.0
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Slope (mrad) Deflection (microns)
-0.273 0.0
-0.273 -0.3
-0.273 -0.5
-0.272 -0.8
-0.272 -1.1
-0.271 -1.4-0.270 -1.6
-0.269 -1.9
-0.267 -2.2
-0.265 -2.4
-0.264 -2.7
-0.262 -3.0
-0.259 -3.2
-0.257 -3.5
-0.254 -3.7
-0.252 -4.0
-0.249 -4.2
-0.245 -4.5-0.242 -4.7
-0.238 -5.0
-0.235 -5.2
-0.231 -5.4
-0.226 -5.7
-0.222 -5.9
-0.218 -6.1
-0.213 -6.3
-0.208 -6.5
-0.203 -6.7
-0.197 -6.9
-0.192 -7.1
-0.186 -7.3
-0.180 -7.5
-0.173 -7.7
-0.167 -7.9
-0.161 -8.0
-0.154 -8.2
-0.147 -8.3
-0.140 -8.5
-0.132 -8.6
-0.125 -8.7
-0.117 -8.9
-0.109 -9.0
-0.101 -9.1-0.093 -9.2
-0.084 -9.3
-0.075 -9.3
-0.066 -9.4
-0.057 -9.5
-0.048 -9.5
-0.039 -9.6
-0.029 -9.6
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-0.019 -9.6
-0.009 -9.6
0.001 -9.6
0.011 -9.6
0.021 -9.6
0.031 -9.6
0.041 -9.60.051 -9.5
0.061 -9.5
0.071 -9.4
0.081 -9.3
0.091 -9.2
0.101 -9.1
0.111 -9.0
0.121 -8.9
0.131 -8.8
0.140 -8.6
0.150 -8.5
0.159 -8.30.168 -8.2
0.177 -8.0
0.186 -7.8
0.195 -7.6
0.204 -7.4
0.212 -7.2
0.221 -7.0
0.229 -6.8
0.237 -6.6
0.244 -6.3
0.252 -6.1
0.259 -5.8
0.265 -5.6
0.272 -5.3
0.278 -5.0
0.284 -4.7
0.290 -4.4
0.295 -4.1
0.300 -3.8
0.305 -3.5
0.310 -3.2
0.314 -2.9
0.317 -2.6
0.320 -2.3
0.323 -2.00.326 -1.6
0.328 -1.3
0.329 -1.0
0.330 -0.7
0.331 -0.3
0.331 0.0
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Beam Values
Length, L (mm) 100
Width, W (mm) 25
Height, H (mm) 6
Length increment, Linc (mm) 1
Modulus of elasticity, E (N/mm^2) 200000Moment of inertia, I (mm^4) 450
Distance farthest fiber to nuetral axis, cc (mm) 3
Loading
Point load, F (N) 10
Location of point load, af (mm) 50
Distributed load amplitude, wa, (N/mm) 1
Distributed load amplitude, wL, (N/mm) 1
Starting point of load, aw (mm) 50
Total distributed load (N) 50
Moment load, M (N-mm) 10
Location of moment load, am (mm) 25
Finite Diffrence ProE Mechanica-9.643 -9.848Maximum deflection (microns)
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