beam simply supported

7/27/2019 Beam Simply Supported

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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)


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)


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)


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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beam simply supported

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