Beam Cantilever com

8/6/2019 Beam Cantilever com

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beam_can

To determine deflection of a cantilev

By Alex Slocum, 1/1/04, last mo

Schematic

Beam dimensions and properties 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 from farthest fiber to neutral axis, cc (mm) 3

Loading

Point load, F (N) 10

Location of point load, af (mm) 0

Distributed load amplitude, wa, (N/mm) 1

Distributed load amplitude, wL, (N/mm) 1

Starting point of distributed load, aw (mm) 50

Moment load, M (N-mm) 10

Location of moment load, am (mm) 25

Maximum deflection (microns) -56.771

Maximum slope (milli radians) 0.779

Reactions at beam ends

0.000

60.000

0.000

-2240.000

0.0010.000

-0.057

0.000

Equations

Enters numbers in BO

RA, Ra (N)

RB, Rb (N)

MA, Ma (N)

MB, Mb (N-mm)

A, ta (radians)

B, tb (radians)

A, da (mm)

B, db (mm)

M

wa

aw

af

am

Ax

L


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Note: For other types of distributed loads, use principle of superposition

( )

(2

2

2

3

2 3

2

2

2 2 6

2 6 6

a

af w

w

a w

A A f

f aA AA

fA A

A A

V F x a x awL a

x awM x F x aM R

F x a x awx xM R

EI EI EI EI

F x ax xM Rx

EI EI EI

=

= +

= + +

= + + +

( ) ( ) (

( ) ( ) ( )

( ) ( )(

23

33 2 3

2

2 6 4

2 3

3

6 24

L a w

B B

f L aw

A a

ffw

A a

L aw w F F LR M

F L a L a w ww

EI EI

aF aL L L aw

EI EI

+ = + =

= + +

+ =


3/16

ilever.xls

er beam under superimposed loads

dified 06/11/04 by Xue'en Yang

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 for wa, in mm

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 ARotation at B

Deflection at A

Deflection at B

LD, Results in RED

2

FwL

B


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)

( )( )

( )

( )

3

0

3 4

4 5

6

24

24

w

L a w

m

w

L aw w m

w

a L aw

x awM x a

L a

x a M x aw w

EI L a EI

x a x aw w

EI

+

+

( )

2

120 2

w m

w

M x a

EI L a EI

+

) ( ) ( )

( )

)( ) ( ) ( )

2

22

2 3

4

5 2

L aw

af

w

mL a w

w

L a w wa Mw

M L a

EI

M aLL aw wa

EI

+ +

++ + +


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0 10 20 30 40 50 60 70 80 90 100

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

Deflection

Distance from left end of beam (mm)

Deflection(m

crons)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

Slope(millir a

dians)

0 10 20 30 40 50 60 70 80 90 100

-2500

-2000

-1500

-1000

-500

0

Moment


Moment(N-m

m)

-16.0

-14.0

-12.0

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

Stress(Pa)

-20

-10

0

Transverse Shear

(N)


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0 10 20 30 40 50 60 70 80 90 100

-70

-60

-50

-40

-30


TransverseS

hear


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0 10 20 30 40 50 60 70 80 90 100

Slope


10 20 30 40 50 60 70 80 90 100

Stress



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Distance along beam, x Shear (N) Moment (N-mm) Stress (Pa) Slope (mrad)

0 0 0 0.0 0.779

1 -10 -10 -0.1 0.779

2 -10 -20 -0.1 0.778

3 -10 -30 -0.2 0.778

4 -10 -40 -0.3 0.778

5 -10 -50 -0.3 0.7776 -10 -60 -0.4 0.777

7 -10 -70 -0.5 0.776

8 -10 -80 -0.5 0.775

9 -10 -90 -0.6 0.774

10 -10 -100 -0.7 0.773

11 -10 -110 -0.7 0.772

12 -10 -120 -0.8 0.771

13 -10 -130 -0.9 0.769

14 -10 -140 -0.9 0.768

15 -10 -150 -1.0 0.766

16 -10 -160 -1.1 0.764

17 -10 -170 -1.1 0.76318 -10 -180 -1.2 0.761

19 -10 -190 -1.3 0.759

20 -10 -200 -1.3 0.756

21 -10 -210 -1.4 0.754

22 -10 -220 -1.5 0.752

23 -10 -230 -1.5 0.749

24 -10 -240 -1.6 0.747

25 -10 -250 -1.7 0.744

26 -10 -250 -1.7 0.741

27 -10 -260 -1.7 0.738

28 -10 -270 -1.8 0.735

29 -10 -280 -1.9 0.73230 -10 -290 -1.9 0.729

31 -10 -300 -2.0 0.726

32 -10 -310 -2.1 0.723

33 -10 -320 -2.1 0.719

34 -10 -330 -2.2 0.715

35 -10 -340 -2.3 0.712

36 -10 -350 -2.3 0.708

37 -10 -360 -2.4 0.704

38 -10 -370 -2.5 0.700

39 -10 -380 -2.5 0.696

40 -10 -390 -2.6 0.691

41 -10 -400 -2.7 0.68742 -10 -410 -2.7 0.683

43 -10 -420 -2.8 0.678

44 -10 -430 -2.9 0.673

45 -10 -440 -2.9 0.668

46 -10 -450 -3.0 0.663

47 -10 -460 -3.1 0.658

48 -10 -470 -3.1 0.653

49 -10 -480 -3.2 0.648


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50 -10 -490 -3.3 0.643

51 -11 -501 -3.3 0.637

52 -12 -512 -3.4 0.631

53 -13 -525 -3.5 0.626

54 -14 -538 -3.6 0.620

55 -15 -553 -3.7 0.614

56 -16 -568 -3.8 0.60857 -17 -585 -3.9 0.601

58 -18 -602 -4.0 0.595

59 -19 -621 -4.1 0.588

60 -20 -640 -4.3 0.581

61 -21 -661 -4.4 0.574

62 -22 -682 -4.5 0.566

63 -23 -705 -4.7 0.558

64 -24 -728 -4.9 0.550

65 -25 -753 -5.0 0.542

66 -26 -778 -5.2 0.534

67 -27 -805 -5.4 0.525

68 -28 -832 -5.5 0.51669 -29 -861 -5.7 0.506

70 -30 -890 -5.9 0.497

71 -31 -921 -6.1 0.487

72 -32 -952 -6.3 0.476

73 -33 -985 -6.6 0.465

74 -34 -1018 -6.8 0.454

75 -35 -1053 -7.0 0.443

76 -36 -1088 -7.3 0.431

77 -37 -1125 -7.5 0.419

78 -38 -1162 -7.7 0.406

79 -39 -1201 -8.0 0.393

80 -40 -1240 -8.3 0.37981 -41 -1281 -8.5 0.365

82 -42 -1322 -8.8 0.351

83 -43 -1365 -9.1 0.336

84 -44 -1408 -9.4 0.320

85 -45 -1453 -9.7 0.305

86 -46 -1498 -10.0 0.288

87 -47 -1545 -10.3 0.271

88 -48 -1592 -10.6 0.254

89 -49 -1641 -10.9 0.236

90 -50 -1690 -11.3 0.217

91 -51 -1741 -11.6 0.198

92 -52 -1792 -11.9 0.17993 -53 -1845 -12.3 0.159

94 -54 -1898 -12.7 0.138

95 -55 -1953 -13.0 0.116

96 -56 -2008 -13.4 0.094

97 -57 -2065 -13.8 0.072

98 -58 -2122 -14.1 0.048

99 -59 -2181 -14.5 0.025

100 -60 -2240 -14.9 0.000


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Deflection (microns)

-56.8

-56.0

-55.2

-54.4

-53.7

-52.9-52.1

-51.3

-50.6

-49.8

-49.0

-48.2

-47.5

-46.7

-45.9

-45.2

-44.4

-43.6-42.9

-42.1

-41.3

-40.6

-39.8

-39.1

-38.3

-37.6

-36.8

-36.1

-35.4

-34.6-33.9

-33.2

-32.5

-31.7

-31.0

-30.3

-29.6

-28.9

-28.2

-27.5

-26.8

-26.1-25.4

-24.7

-24.1

-23.4

-22.7

-22.1

-21.4

-20.8


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Beam dimensions and properties Values ProE Mechanica

Length, L (mm) 100 100

Width, W (mm) 25 25

Height, H (mm) 6 6

Length increment, Linc (mm) 1 1

Modulus of elasticity, E (N/mm^2) 200000 200000Moment of inertia, I (mm^4) 450 450

Distance from farthest fiber to neutral axis, cc (mm) 3 3

Loading Condition

Point load, F (N) 10 10

Location of point load, af (mm) 0 0

Distributed load amplitude, wa, (N/mm) 1 1

Distributed load amplitude, wL, (N/mm) 1 1

Starting point of distributed load, aw (mm) 50 50

Moment load, M (N-mm) 10 10

Location of moment load, am (mm) 25 25

Maximum deflection (microns) -56.771 -56.02

Maximum slope (milli radians) 0.779Reactions at beam ends

0.000 0

60.000 60

0.000 0

-2240.000 -2238

0.001

0.000 0

-0.057 -0.06

0.000 0

RA, Ra (N)

RB, Rb (N)

MA, Ma (N)

MB, Mb (N-mm)

A, ta (radians)

B, tb (radians)

A, da (mm)

B, db (mm)


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