Report (Determined Beams & Maxwell Theorem)

In the name of God

2012-04

Mechanics of Material

Laboratory Report

Determined Beams AND Maxwell Theorem

Instructor: Mr. Sabbaghi

Prepared by: Seyed Ali Fatemi

1

Brief Contents:

Introduction ---------------------------------------------------------------------------------- 2

First Stage ------------------------------------------------------------------------------------- 2

Second Stage---------------------------------------------------------------------------------- 5

Part 1 ------------------------------------------------------------------------------------------- 7

A ------------------------------------------------------------------------------------------------- 8

B ------------------------------------------------------------------------------------------------ 58

C ---------------------------------------------------------------------------------------------- 108

D ---------------------------------------------------------------------------------------------- 158

E ---------------------------------------------------------------------------------------------- 208

F ---------------------------------------------------------------------------------------------- 258

Part 2 ---------------------------------------------------------------------------------------- 308

Results and Questions ------------------------------------------------------------------ 322

At Last --------------------------------------------------------------------------------------- 329

2

Introduction:

In this report, our aim is to study the reactions of determined beams under

concentrated loads. At first stage we’ll explain the term “determined beam”,

then the experiment procedure will be illustrated and it will be answered that

actually why we examine determined beams. In the next stage the diagrams and

data will be presented. Practical and theoretical and error altitudes will be

illustrated in tables. At last the specified questions will be answered. “IT SLOULD

BE POINTED THAT THE NUMBERS ARE FIXED IN TWO DIGITS.”

First Stage:

One of the most common structural members is a beam. A beam is designed

to resist forces that act laterally to the longitudinal axis of the member. In order

to analyze or design a beam, the forces that are developed internally in the

material must first be determined. One very useful technique for rapidly

determining the internal forces is through the construction of shear force and

bending moment diagrams. Shear force is the internal force acting on a plane

perpendicular to the longitudinal axis of the beam. Bending moment is the

3

internal moment rotating about an axis perpendicular to the longitudinal axis.

For beams that can be fully described in two dimensions, the internal moment

acts about an axis that is normal to the plane of the beam and the applied loads.

The Beam module considers statically determinate beams. Statically

determinate beams generally fall into two types: simply supported spans and

cantilever spans. Simple supports restrain translation of the beam but do not

restrict the rotation of the beam. Simple beam reactions consist of vertical or

horizontal forces. Cantilever supports restrain both translation and rotation of

the beam, and the cantilever beam reactions consist of vertical and horizontal

forces plus a moment. The Beam module is limited to beams without internal

pins, and therefore, a maximum of three support reactions can be computed

from the three equilibrium equations.

Once the type and location of the supports is defined, the shear force and

bending moment diagrams can be constructed for the loads applied to the

beam. These diagrams graphically depict the variation of shear force and

internal bending moment at all points along the length of the beam. From these

plots, the extreme values of shear and moment can be readily established.

Both normal and shear stresses are produced in a beam. Beam normal

stresses are computed from the flexure formula, which relates the internal

4

moment and the beam cross-sectional properties to the normal stress.

Transverse shear stresses are computed from the shear formula for beams,

which relates the internal shear force and the beam cross-sectional properties to

the shear stress. The internal forces and moments used to compute the shear

stress and normal stress can be found from the shear force and bending

moment diagrams.

If the material properties and dimensions of the beam cross-section are

defined, the deflected shape of the beam can also be determined. Beam

deflections may be an important consideration in deciding whether a beam will

perform satisfactorily in the intended application.

In these experiments by considering the beam material and section of area

and adding forces on beam, the deflection will be studied. This will help to show

the difference between the practical and theoretical deflections of several

beams. The experiments are in two parts:

CL: Constant Load location

CD: Constant Deflectometer’s location

For each material, both parts will be presented.

5

Second Stage:

Number Material Dimensions (mm) E (GPa)

A Aluminum 6061-T6 19.5*4*600 68.90

B Brass C83400 30*4*600 101

C Brass C83400 20*4*500 101

D Brass C83400 25*4*500 101

E Steel st37

structural

25*3*600 200

F Steel st37

structural

25*4*500 200

Diagram structure

Beam diagram

Shear stress

diagram

Moment diagram

Slope diagram

Deflection Table

6

Examination Parts

PART1: Determined Beams

PART2: Maxwell Theorem

8

A)CL) 200g)

9

For the shear discontinuity equation, the following units are displayed:

Length units = mm

Force units = N Moment units = N-mm

Shear discontinuity equation using symbolic notations:

Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0

Shear discontinuity equation showing actual numeric values:

Shear = +0.82<x-0.00>0 +1.14<x-600.00>0 - 1.96<x-350.00>0

When using discontinuity functions, if the term in the < > brackets is negative for a particular value of x, the quantity in the < > brackets is defined to have a

value of zero.

For the moment discontinuity equation, the following units are displayed: Length units = mm


Moment discontinuity equation using symbolic notations:

Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1

Moment discontinuity equation showing actual numeric values:

Moment = +0.82<x-0.00>1 +1.14<x-600.00>1 - 1.96<x-350.00>1


value of zero.

For the slope discontinuity equation, the following units are displayed: Length units = mm

Force units = N

Moment units = N-mm EI = +7,165,598.49 N-mm²

Slope discontinuity equation using symbolic notations:

10

EI × Slope = Ay/2<x-0.00>2 +By/2<x-600.00>2 - (Slope at x=0) - P1/2<x-

350.00>2

Slope discontinuity equation showing actual numeric values:

EI × Slope = +0.82/2<x-0.00>2 +1.14/2<x-600.00>2 - 40,534.38- 1.96/2<x-

350.00>2

Note: Slope computed from this equation is in units of radians.


value of zero.

For the deflection discontinuity equation, the following units are displayed: Length units = mm


EI = +7,165,598.49 N-mm²

Deflection discontinuity equation using symbolic notations:

EI × Deflection = Ay/6<x-0.00>3 +By/6<x-600.00>3 - (Slope at x=0) x -

P1/6<x-350.00>3

Deflection discontinuity equation showing actual numeric values:

EI × Deflection = +0.82/6<x-0.00>3 +1.14/6<x-600.00>3 - 40,534.38x-

1.96/6<x-350.00>3

Note: Deflection computed from this equation is in units of mm.


value of zero.

11

400g)

12

For the shear discontinuity equation, the following units are displayed: Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +1.64<x-0.00>0 +2.29<x-600.00>0 - 3.92<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +1.64<x-0.00>1 +2.29<x-600.00>1 - 3.92<x-350.00>1

When using discontinuity functions, if the term in the < > brackets is negative

for a particular value of x, the quantity in the < > brackets is defined to have a value of zero.

For the slope discontinuity equation, the following units are displayed:

Length units = mm Force units = N



13


350.00>2


EI × Slope = +1.64/2<x-0.00>2 +2.29/2<x-600.00>2 - 81,068.75- 3.92/2<x-

350.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-350.00>3



3.92/6<x-350.00>3



value of zero.

14

600g)

15


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +2.45<x-0.00>0 +3.43<x-600.00>0 - 5.89<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +2.45<x-0.00>1 +3.43<x-600.00>1 - 5.89<x-350.00>1


value of zero.


Force units = N



16


350.00>2


EI × Slope = +2.45/2<x-0.00>2 +3.43/2<x-600.00>2 - 121,603.13-

5.89/2<x-350.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-350.00>3



5.89/6<x-350.00>3



value of zero.

17

800g)

18


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +3.27<x-0.00>0 +4.58<x-600.00>0 - 7.85<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +3.27<x-0.00>1 +4.58<x-600.00>1 - 7.85<x-350.00>1


value of zero.


Force units = N



19


350.00>2


EI × Slope = +3.27/2<x-0.00>2 +4.58/2<x-600.00>2 - 162,137.50-

7.85/2<x-350.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-350.00>3



7.85/6<x-350.00>3



value of zero.

21

A)CD) 200g)@100mm

22


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +1.64<x-0.00>0 +0.33<x-600.00>0 - 1.96<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +1.64<x-0.00>1 +0.33<x-600.00>1 - 1.96<x-100.00>1


value of zero.


Force units = N



23


100.00>2


EI × Slope = +1.64/2<x-0.00>2 +0.33/2<x-600.00>2 - 29,975.00- 1.96/2<x-

100.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-100.00>3



1.96/6<x-100.00>3



value of zero.

24

200g)@200mm

25


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +1.31<x-0.00>0 +0.65<x-600.00>0 - 1.96<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +1.31<x-0.00>1 +0.65<x-600.00>1 - 1.96<x-200.00>1


value of zero.


Force units = N



26


200.00>2


EI × Slope = +1.31/2<x-0.00>2 +0.65/2<x-600.00>2 - 43,600.00- 1.96/2<x-

200.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-200.00>3



1.96/6<x-200.00>3



value of zero.

27

200g)@500mm

28


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.33<x-0.00>0 +1.64<x-600.00>0 - 1.96<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.33<x-0.00>1 +1.64<x-600.00>1 - 1.96<x-500.00>1


value of zero.


Force units = N



29


500.00>2


EI × Slope = +0.33/2<x-0.00>2 +1.64/2<x-600.00>2 - 19,075.00- 1.96/2<x-

500.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-500.00>3



1.96/6<x-500.00>3



value of zero.

30

400g)@100mm

31


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +3.27<x-0.00>0 +0.65<x-600.00>0 - 3.92<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +3.27<x-0.00>1 +0.65<x-600.00>1 - 3.92<x-100.00>1


value of zero.


Force units = N



32


100.00>2


EI × Slope = +3.27/2<x-0.00>2 +0.65/2<x-600.00>2 - 59,950.00- 3.92/2<x-

100.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-100.00>3



3.92/6<x-100.00>3



value of zero.

33

400g)@200mm

34


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +2.62<x-0.00>0 +1.31<x-600.00>0 - 3.92<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +2.62<x-0.00>1 +1.31<x-600.00>1 - 3.92<x-200.00>1


value of zero.


Force units = N



35


200.00>2


EI × Slope = +2.62/2<x-0.00>2 +1.31/2<x-600.00>2 - 87,200.00- 3.92/2<x-

200.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-200.00>3



3.92/6<x-200.00>3



value of zero.

36

400g)@500mm

37


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.65<x-0.00>0 +3.27<x-600.00>0 - 3.92<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.65<x-0.00>1 +3.27<x-600.00>1 - 3.92<x-500.00>1


value of zero.


Force units = N



38


500.00>2


EI × Slope = +0.65/2<x-0.00>2 +3.27/2<x-600.00>2 - 38,150.00- 3.92/2<x-

500.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-500.00>3



3.92/6<x-500.00>3



value of zero.

39

600g)@100mm

40


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +4.91<x-0.00>0 +0.98<x-600.00>0 - 5.89<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +4.91<x-0.00>1 +0.98<x-600.00>1 - 5.89<x-100.00>1


value of zero.


Force units = N



41


100.00>2


EI × Slope = +4.91/2<x-0.00>2 +0.98/2<x-600.00>2 - 89,925.00- 5.89/2<x-

100.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-100.00>3



5.89/6<x-100.00>3



value of zero.

42

600g)@200mm

43


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +3.92<x-0.00>0 +1.96<x-600.00>0 - 5.89<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +3.92<x-0.00>1 +1.96<x-600.00>1 - 5.89<x-200.00>1


value of zero.


Force units = N



44


200.00>2


EI × Slope = +3.92/2<x-0.00>2 +1.96/2<x-600.00>2 - 130,800.00-

5.89/2<x-200.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-200.00>3



5.89/6<x-200.00>3



value of zero.

45

600g)@500mm

46


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.98<x-0.00>0 +4.91<x-600.00>0 - 5.89<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.98<x-0.00>1 +4.91<x-600.00>1 - 5.89<x-500.00>1


value of zero.


Force units = N



47


500.00>2


EI × Slope = +0.98/2<x-0.00>2 +4.91/2<x-600.00>2 - 57,225.00- 5.89/2<x-

500.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-500.00>3



5.89/6<x-500.00>3



value of zero.

48

800g)@100mm

49


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +6.54<x-0.00>0 +1.31<x-600.00>0 - 7.85<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +6.54<x-0.00>1 +1.31<x-600.00>1 - 7.85<x-100.00>1


value of zero.


Force units = N



50


100.00>2


EI × Slope = +6.54/2<x-0.00>2 +1.31/2<x-600.00>2 - 119,900.00-

7.85/2<x-100.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-100.00>3



7.85/6<x-100.00>3



value of zero.

51

800g)@200mm

52


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +5.23<x-0.00>0 +2.62<x-600.00>0 - 7.85<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +5.23<x-0.00>1 +2.62<x-600.00>1 - 7.85<x-200.00>1


value of zero.


Force units = N



53


200.00>2


EI × Slope = +5.23/2<x-0.00>2 +2.62/2<x-600.00>2 - 174,400.00-

7.85/2<x-200.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-200.00>3



7.85/6<x-200.00>3



value of zero.

54

800g)@500mm

55


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +1.31<x-0.00>0 +6.54<x-600.00>0 - 7.85<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +1.31<x-0.00>1 +6.54<x-600.00>1 - 7.85<x-500.00>1


value of zero.


Force units = N



56


500.00>2


EI × Slope = +1.31/2<x-0.00>2 +6.54/2<x-600.00>2 - 76,300.00- 7.85/2<x-

500.00>2



value of zero.



EI = +7,165,598.49 N-mm²



P1/6<x-500.00>3



7.85/6<x-500.00>3



value of zero.

58

B)CL) 200g)

59


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +0.82<x-0.00>0 +1.14<x-600.00>0 - 1.96<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +0.82<x-0.00>1 +1.14<x-600.00>1 - 1.96<x-350.00>1


value of zero.


Force units = N



60


350.00>2


EI × Slope = +0.82/2<x-0.00>2 +1.14/2<x-600.00>2 - 40,534.38- 1.96/2<x-

350.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-350.00>3



1.96/6<x-350.00>3



value of zero.

61

400g)

62


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +1.64<x-0.00>0 +2.29<x-600.00>0 - 3.92<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +1.64<x-0.00>1 +2.29<x-600.00>1 - 3.92<x-350.00>1


value of zero.


Force units = N



63


350.00>2


EI × Slope = +1.64/2<x-0.00>2 +2.29/2<x-600.00>2 - 81,068.75- 3.92/2<x-

350.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-350.00>3



3.92/6<x-350.00>3



value of zero.

64

600g)

65


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +2.45<x-0.00>0 +3.43<x-600.00>0 - 5.89<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +2.45<x-0.00>1 +3.43<x-600.00>1 - 5.89<x-350.00>1


value of zero.


Force units = N



66


350.00>2


EI × Slope = +2.45/2<x-0.00>2 +3.43/2<x-600.00>2 - 121,603.13-

5.89/2<x-350.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-350.00>3



5.89/6<x-350.00>3



value of zero.

67

800g)

68


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +3.27<x-0.00>0 +4.58<x-600.00>0 - 7.85<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +3.27<x-0.00>1 +4.58<x-600.00>1 - 7.85<x-350.00>1


value of zero.


Force units = N



69


350.00>2


EI × Slope = +3.27/2<x-0.00>2 +4.58/2<x-600.00>2 - 162,137.50-

7.85/2<x-350.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-350.00>3



7.85/6<x-350.00>3



value of zero.

71

B)CD) 200g)@100mm

72


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +1.64<x-0.00>0 +0.33<x-600.00>0 - 1.96<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +1.64<x-0.00>1 +0.33<x-600.00>1 - 1.96<x-100.00>1


value of zero.


Force units = N



73


100.00>2


EI × Slope = +1.64/2<x-0.00>2 +0.33/2<x-600.00>2 - 29,975.00- 1.96/2<x-

100.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-100.00>3



1.96/6<x-100.00>3



value of zero.

74

200g)@200mm

75


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +1.31<x-0.00>0 +0.65<x-600.00>0 - 1.96<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +1.31<x-0.00>1 +0.65<x-600.00>1 - 1.96<x-200.00>1


value of zero.


Force units = N



76


200.00>2


EI × Slope = +1.31/2<x-0.00>2 +0.65/2<x-600.00>2 - 43,600.00- 1.96/2<x-

200.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-200.00>3



1.96/6<x-200.00>3



value of zero.

77

200g)@500mm

78


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.33<x-0.00>0 +1.64<x-600.00>0 - 1.96<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.33<x-0.00>1 +1.64<x-600.00>1 - 1.96<x-500.00>1


value of zero.


Force units = N



79


500.00>2


EI × Slope = +0.33/2<x-0.00>2 +1.64/2<x-600.00>2 - 19,075.00- 1.96/2<x-

500.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-500.00>3



1.96/6<x-500.00>3



value of zero.

80

400g)@100mm

81


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +3.27<x-0.00>0 +0.65<x-600.00>0 - 3.92<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +3.27<x-0.00>1 +0.65<x-600.00>1 - 3.92<x-100.00>1


value of zero.


Force units = N



82


100.00>2


EI × Slope = +3.27/2<x-0.00>2 +0.65/2<x-600.00>2 - 59,950.00- 3.92/2<x-

100.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-100.00>3



3.92/6<x-100.00>3



value of zero.

83

400g)@200mm

84


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +2.62<x-0.00>0 +1.31<x-600.00>0 - 3.92<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +2.62<x-0.00>1 +1.31<x-600.00>1 - 3.92<x-200.00>1


value of zero.


Force units = N



85


200.00>2


EI × Slope = +2.62/2<x-0.00>2 +1.31/2<x-600.00>2 - 87,200.00- 3.92/2<x-

200.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-200.00>3



3.92/6<x-200.00>3



value of zero.

86

400g)@500mm

87


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.65<x-0.00>0 +3.27<x-600.00>0 - 3.92<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.65<x-0.00>1 +3.27<x-600.00>1 - 3.92<x-500.00>1


value of zero.


Force units = N



88


500.00>2


EI × Slope = +0.65/2<x-0.00>2 +3.27/2<x-600.00>2 - 38,150.00- 3.92/2<x-

500.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-500.00>3



3.92/6<x-500.00>3



value of zero.

89

600g)@100mm

90


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +4.91<x-0.00>0 +0.98<x-600.00>0 - 5.89<x-100.00>0


value of zero.

For the moment discontinuity equation, the following units are displayed:

Length units = mm Force units = N

Moment units = N-mm


Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +4.91<x-0.00>1 +0.98<x-600.00>1 - 5.89<x-100.00>1


value of zero.



EI = +16,159,996.60 N-mm²


91


100.00>2


EI × Slope = +4.91/2<x-0.00>2 +0.98/2<x-600.00>2 - 89,925.00- 5.89/2<x-

100.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-100.00>3



5.89/6<x-100.00>3



value of zero.

92

600g)@200mm

93


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +3.92<x-0.00>0 +1.96<x-600.00>0 - 5.89<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +3.92<x-0.00>1 +1.96<x-600.00>1 - 5.89<x-200.00>1


value of zero.


Force units = N



94


200.00>2


EI × Slope = +3.92/2<x-0.00>2 +1.96/2<x-600.00>2 - 130,800.00-

5.89/2<x-200.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-200.00>3



5.89/6<x-200.00>3



value of zero.

95

600g)@500mm

96


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.98<x-0.00>0 +4.91<x-600.00>0 - 5.89<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.98<x-0.00>1 +4.91<x-600.00>1 - 5.89<x-500.00>1


value of zero.


Force units = N



97


500.00>2


EI × Slope = +0.98/2<x-0.00>2 +4.91/2<x-600.00>2 - 57,225.00- 5.89/2<x-

500.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-500.00>3



5.89/6<x-500.00>3



value of zero.

98

800g)@100mm

99


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +6.54<x-0.00>0 +1.31<x-600.00>0 - 7.85<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +6.54<x-0.00>1 +1.31<x-600.00>1 - 7.85<x-100.00>1


value of zero.


Force units = N



100


100.00>2


EI × Slope = +6.54/2<x-0.00>2 +1.31/2<x-600.00>2 - 119,900.00-

7.85/2<x-100.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-100.00>3



7.85/6<x-100.00>3



value of zero.

101

800g)@200mm

102


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +5.23<x-0.00>0 +2.62<x-600.00>0 - 7.85<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +5.23<x-0.00>1 +2.62<x-600.00>1 - 7.85<x-200.00>1


value of zero.


Force units = N



103


200.00>2


EI × Slope = +5.23/2<x-0.00>2 +2.62/2<x-600.00>2 - 174,400.00-

7.85/2<x-200.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-200.00>3



7.85/6<x-200.00>3



value of zero.

104

800g)@500mm

105


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +1.31<x-0.00>0 +6.54<x-600.00>0 - 7.85<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +1.31<x-0.00>1 +6.54<x-600.00>1 - 7.85<x-500.00>1


value of zero.


Force units = N



106


500.00>2


EI × Slope = +1.31/2<x-0.00>2 +6.54/2<x-600.00>2 - 76,300.00- 7.85/2<x-

500.00>2



value of zero.



EI = +16,159,996.60 N-mm²



P1/6<x-500.00>3



7.85/6<x-500.00>3



value of zero.

108

C)CL) 200g)

109


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +0.98<x-0.00>0 +0.98<x-500.00>0 - 1.96<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +0.98<x-0.00>1 +0.98<x-500.00>1 - 1.96<x-250.00>1


value of zero.


Force units = N



110


250.00>2


EI × Slope = +0.98/2<x-0.00>2 +0.98/2<x-500.00>2 - 30,656.25- 1.96/2<x-

250.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-250.00>3



1.96/6<x-250.00>3



value of zero.

111

400g)

112


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +1.96<x-0.00>0 +1.96<x-500.00>0 - 3.92<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +1.96<x-0.00>1 +1.96<x-500.00>1 - 3.92<x-250.00>1


value of zero.


Force units = N



113


250.00>2


EI × Slope = +1.96/2<x-0.00>2 +1.96/2<x-500.00>2 - 61,312.50- 3.92/2<x-

250.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-250.00>3



3.92/6<x-250.00>3



value of zero.

114

600g)

115


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +2.94<x-0.00>0 +2.94<x-500.00>0 - 5.89<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +2.94<x-0.00>1 +2.94<x-500.00>1 - 5.89<x-250.00>1


value of zero.


Force units = N



116


250.00>2


EI × Slope = +2.94/2<x-0.00>2 +2.94/2<x-500.00>2 - 91,968.75- 5.89/2<x-

250.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-250.00>3



5.89/6<x-250.00>3



value of zero.

117

800g)

118


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +3.92<x-0.00>0 +3.92<x-500.00>0 - 7.85<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +3.92<x-0.00>1 +3.92<x-500.00>1 - 7.85<x-250.00>1


value of zero.


Force units = N



119


250.00>2


EI × Slope = +3.92/2<x-0.00>2 +3.92/2<x-500.00>2 - 122,625.00-

7.85/2<x-250.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-250.00>3



7.85/6<x-250.00>3



value of zero.

121

C)CD) 200g)@100mm

122


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +1.57<x-0.00>0 +0.39<x-500.00>0 - 1.96<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +1.57<x-0.00>1 +0.39<x-500.00>1 - 1.96<x-100.00>1


value of zero.


Force units = N



123


100.00>2


EI × Slope = +1.57/2<x-0.00>2 +0.39/2<x-500.00>2 - 23,544.00- 1.96/2<x-

100.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-100.00>3



1.96/6<x-100.00>3



value of zero.

124

200g)@200mm

125


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +1.18<x-0.00>0 +0.78<x-500.00>0 - 1.96<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +1.18<x-0.00>1 +0.78<x-500.00>1 - 1.96<x-200.00>1


value of zero.


Force units = N



126


200.00>2


EI × Slope = +1.18/2<x-0.00>2 +0.78/2<x-500.00>2 - 31,392.00- 1.96/2<x-

200.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-200.00>3



1.96/6<x-200.00>3



value of zero.

127

200g)@400mm

128


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +0.39<x-0.00>0 +1.57<x-500.00>0 - 1.96<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +0.39<x-0.00>1 +1.57<x-500.00>1 - 1.96<x-400.00>1


value of zero.


Force units = N



129


400.00>2


EI × Slope = +0.39/2<x-0.00>2 +1.57/2<x-500.00>2 - 15,696.00- 1.96/2<x-

400.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-400.00>3



1.96/6<x-400.00>3



value of zero.

130

400g)@100mm

131


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +3.14<x-0.00>0 +0.78<x-500.00>0 - 3.92<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +3.14<x-0.00>1 +0.78<x-500.00>1 - 3.92<x-100.00>1


value of zero.


Force units = N



132


100.00>2


EI × Slope = +3.14/2<x-0.00>2 +0.78/2<x-500.00>2 - 47,088.00- 3.92/2<x-

100.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-100.00>3



3.92/6<x-100.00>3



value of zero.

133

400g)@200mm

134


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +2.35<x-0.00>0 +1.57<x-500.00>0 - 3.92<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +2.35<x-0.00>1 +1.57<x-500.00>1 - 3.92<x-200.00>1


value of zero.


Force units = N



135


200.00>2


EI × Slope = +2.35/2<x-0.00>2 +1.57/2<x-500.00>2 - 62,784.00- 3.92/2<x-

200.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-200.00>3



3.92/6<x-200.00>3



value of zero.

136

400g)@400mm

137


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +0.78<x-0.00>0 +3.14<x-500.00>0 - 3.92<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +0.78<x-0.00>1 +3.14<x-500.00>1 - 3.92<x-400.00>1


value of zero.


Force units = N



138


400.00>2


EI × Slope = +0.78/2<x-0.00>2 +3.14/2<x-500.00>2 - 31,392.00- 3.92/2<x-

400.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-400.00>3



3.92/6<x-400.00>3



value of zero.

139

600g)@100mm

140


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +4.71<x-0.00>0 +1.18<x-500.00>0 - 5.89<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +4.71<x-0.00>1 +1.18<x-500.00>1 - 5.89<x-100.00>1


value of zero.


Force units = N



141


100.00>2


EI × Slope = +4.71/2<x-0.00>2 +1.18/2<x-500.00>2 - 70,632.00- 5.89/2<x-

100.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-100.00>3



5.89/6<x-100.00>3



value of zero.

142

600g)@200mm

143


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +3.53<x-0.00>0 +2.35<x-500.00>0 - 5.89<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +3.53<x-0.00>1 +2.35<x-500.00>1 - 5.89<x-200.00>1


value of zero.


Force units = N



144


200.00>2


EI × Slope = +3.53/2<x-0.00>2 +2.35/2<x-500.00>2 - 94,176.00- 5.89/2<x-

200.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-200.00>3



5.89/6<x-200.00>3



value of zero.

145

600g)@400mm

146


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +1.18<x-0.00>0 +4.71<x-500.00>0 - 5.89<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +1.18<x-0.00>1 +4.71<x-500.00>1 - 5.89<x-400.00>1


value of zero.


Force units = N



147


400.00>2


EI × Slope = +1.18/2<x-0.00>2 +4.71/2<x-500.00>2 - 47,088.00- 5.89/2<x-

400.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-400.00>3



5.89/6<x-400.00>3



value of zero.

148

800g)@100mm

149


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +6.28<x-0.00>0 +1.57<x-500.00>0 - 7.85<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +6.28<x-0.00>1 +1.57<x-500.00>1 - 7.85<x-100.00>1


value of zero.


Force units = N



150


100.00>2


EI × Slope = +6.28/2<x-0.00>2 +1.57/2<x-500.00>2 - 94,176.00- 7.85/2<x-

100.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-100.00>3



7.85/6<x-100.00>3



value of zero.

151

800g)@200mm

152


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +4.71<x-0.00>0 +3.14<x-500.00>0 - 7.85<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +4.71<x-0.00>1 +3.14<x-500.00>1 - 7.85<x-200.00>1


value of zero.


Force units = N



153


200.00>2


EI × Slope = +4.71/2<x-0.00>2 +3.14/2<x-500.00>2 - 125,568.00-

7.85/2<x-200.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-200.00>3



7.85/6<x-200.00>3



value of zero.

154

800g)@400mm

155


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +1.57<x-0.00>0 +6.28<x-500.00>0 - 7.85<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +1.57<x-0.00>1 +6.28<x-500.00>1 - 7.85<x-400.00>1


value of zero.


Force units = N



156


400.00>2


EI × Slope = +1.57/2<x-0.00>2 +6.28/2<x-500.00>2 - 62,784.00- 7.85/2<x-

400.00>2



value of zero.



EI = +10,773,331.06 N-mm²



P1/6<x-400.00>3



7.85/6<x-400.00>3



value of zero.

158

D)CL) 200g)

159


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +0.98<x-0.00>0 +0.98<x-500.00>0 - 1.96<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +0.98<x-0.00>1 +0.98<x-500.00>1 - 1.96<x-250.00>1


value of zero.


Force units = N



160


250.00>2


EI × Slope = +0.98/2<x-0.00>2 +0.98/2<x-500.00>2 - 30,656.25- 1.96/2<x-

250.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-250.00>3



1.96/6<x-250.00>3



value of zero.

161

400g)

162


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +1.96<x-0.00>0 +1.96<x-500.00>0 - 3.92<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +1.96<x-0.00>1 +1.96<x-500.00>1 - 3.92<x-250.00>1


value of zero.


Force units = N



163


250.00>2


EI × Slope = +1.96/2<x-0.00>2 +1.96/2<x-500.00>2 - 61,312.50- 3.92/2<x-

250.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-250.00>3



3.92/6<x-250.00>3



value of zero.

164

600g)

165


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +2.94<x-0.00>0 +2.94<x-500.00>0 - 5.89<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +2.94<x-0.00>1 +2.94<x-500.00>1 - 5.89<x-250.00>1


value of zero.


Force units = N



166


250.00>2


EI × Slope = +2.94/2<x-0.00>2 +2.94/2<x-500.00>2 - 91,968.75- 5.89/2<x-

250.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-250.00>3



5.89/6<x-250.00>3



value of zero.

167

800g)

168


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +3.92<x-0.00>0 +3.92<x-500.00>0 - 7.85<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +3.92<x-0.00>1 +3.92<x-500.00>1 - 7.85<x-250.00>1


value of zero.


Force units = N



169


250.00>2


EI × Slope = +3.92/2<x-0.00>2 +3.92/2<x-500.00>2 - 122,625.00-

7.85/2<x-250.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-250.00>3



7.85/6<x-250.00>3



value of zero.

171

D)CD) 200g)@100mm

172


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +1.57<x-0.00>0 +0.39<x-500.00>0 - 1.96<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +1.57<x-0.00>1 +0.39<x-500.00>1 - 1.96<x-100.00>1


value of zero.


Force units = N



173


100.00>2


EI × Slope = +1.57/2<x-0.00>2 +0.39/2<x-500.00>2 - 23,544.00- 1.96/2<x-

100.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-100.00>3



1.96/6<x-100.00>3



value of zero.

174

200g)@200mm

175


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +1.18<x-0.00>0 +0.78<x-500.00>0 - 1.96<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +1.18<x-0.00>1 +0.78<x-500.00>1 - 1.96<x-200.00>1


value of zero.


Force units = N



176


200.00>2


EI × Slope = +1.18/2<x-0.00>2 +0.78/2<x-500.00>2 - 31,392.00- 1.96/2<x-

200.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-200.00>3



1.96/6<x-200.00>3



value of zero.

177

200g)@400mm

178


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +0.39<x-0.00>0 +1.57<x-500.00>0 - 1.96<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +0.39<x-0.00>1 +1.57<x-500.00>1 - 1.96<x-400.00>1


value of zero.


Force units = N



179


400.00>2


EI × Slope = +0.39/2<x-0.00>2 +1.57/2<x-500.00>2 - 15,696.00- 1.96/2<x-

400.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-400.00>3



1.96/6<x-400.00>3



value of zero.

180

400g)@100mm

181


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +3.14<x-0.00>0 +0.78<x-500.00>0 - 3.92<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +3.14<x-0.00>1 +0.78<x-500.00>1 - 3.92<x-100.00>1


value of zero.


Force units = N



182


100.00>2


EI × Slope = +3.14/2<x-0.00>2 +0.78/2<x-500.00>2 - 47,088.00- 3.92/2<x-

100.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-100.00>3



3.92/6<x-100.00>3



value of zero.

183

400g)@200mm

184


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +2.35<x-0.00>0 +1.57<x-500.00>0 - 3.92<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +2.35<x-0.00>1 +1.57<x-500.00>1 - 3.92<x-200.00>1


value of zero.


Force units = N



185


200.00>2


EI × Slope = +2.35/2<x-0.00>2 +1.57/2<x-500.00>2 - 62,784.00- 3.92/2<x-

200.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-200.00>3



3.92/6<x-200.00>3



value of zero.

186

400g)@400mm

187


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +0.78<x-0.00>0 +3.14<x-500.00>0 - 3.92<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +0.78<x-0.00>1 +3.14<x-500.00>1 - 3.92<x-400.00>1


value of zero.


Force units = N



188


400.00>2


EI × Slope = +0.78/2<x-0.00>2 +3.14/2<x-500.00>2 - 31,392.00- 3.92/2<x-

400.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-400.00>3



3.92/6<x-400.00>3



value of zero.

189

600g)@100mm

190


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +4.71<x-0.00>0 +1.18<x-500.00>0 - 5.89<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +4.71<x-0.00>1 +1.18<x-500.00>1 - 5.89<x-100.00>1


value of zero.


Force units = N



191


100.00>2


EI × Slope = +4.71/2<x-0.00>2 +1.18/2<x-500.00>2 - 70,632.00- 5.89/2<x-

100.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-100.00>3



5.89/6<x-100.00>3



value of zero.

192

600g)@200mm

193


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +3.53<x-0.00>0 +2.35<x-500.00>0 - 5.89<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +3.53<x-0.00>1 +2.35<x-500.00>1 - 5.89<x-200.00>1


value of zero.


Force units = N



194


200.00>2


EI × Slope = +3.53/2<x-0.00>2 +2.35/2<x-500.00>2 - 94,176.00- 5.89/2<x-

200.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-200.00>3



5.89/6<x-200.00>3



value of zero.

195

600g)@400mm

196


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +1.18<x-0.00>0 +4.71<x-500.00>0 - 5.89<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +1.18<x-0.00>1 +4.71<x-500.00>1 - 5.89<x-400.00>1


value of zero.


Force units = N



197


400.00>2


EI × Slope = +1.18/2<x-0.00>2 +4.71/2<x-500.00>2 - 47,088.00- 5.89/2<x-

400.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-400.00>3



5.89/6<x-400.00>3



value of zero.

198

800g)@100mm

199


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +6.28<x-0.00>0 +1.57<x-500.00>0 - 7.85<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +6.28<x-0.00>1 +1.57<x-500.00>1 - 7.85<x-100.00>1


value of zero.


Force units = N



200


100.00>2


EI × Slope = +6.28/2<x-0.00>2 +1.57/2<x-500.00>2 - 94,176.00- 7.85/2<x-

100.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-100.00>3



7.85/6<x-100.00>3



value of zero.

201

800g)@200mm

202


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +4.71<x-0.00>0 +3.14<x-500.00>0 - 7.85<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +4.71<x-0.00>1 +3.14<x-500.00>1 - 7.85<x-200.00>1


value of zero.


Force units = N



203


200.00>2


EI × Slope = +4.71/2<x-0.00>2 +3.14/2<x-500.00>2 - 125,568.00-

7.85/2<x-200.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-200.00>3



7.85/6<x-200.00>3



value of zero.

204

800g)@400mm

205


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +1.57<x-0.00>0 +6.28<x-500.00>0 - 7.85<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +1.57<x-0.00>1 +6.28<x-500.00>1 - 7.85<x-400.00>1


value of zero.


Force units = N



206


400.00>2


EI × Slope = +1.57/2<x-0.00>2 +6.28/2<x-500.00>2 - 62,784.00- 7.85/2<x-

400.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-400.00>3



7.85/6<x-400.00>3



value of zero.

208

E)CL) 200g)

209


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +0.82<x-0.00>0 +1.14<x-600.00>0 - 1.96<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +0.82<x-0.00>1 +1.14<x-600.00>1 - 1.96<x-350.00>1


value of zero.


Force units = N



210


350.00>2


EI × Slope = +0.82/2<x-0.00>2 +1.14/2<x-600.00>2 - 40,534.38- 1.96/2<x-

350.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-350.00>3



1.96/6<x-350.00>3



value of zero.

211

400g)

212


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +1.64<x-0.00>0 +2.29<x-600.00>0 - 3.92<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +1.64<x-0.00>1 +2.29<x-600.00>1 - 3.92<x-350.00>1


value of zero.


Force units = N



213


350.00>2


EI × Slope = +1.64/2<x-0.00>2 +2.29/2<x-600.00>2 - 81,068.75- 3.92/2<x-

350.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-350.00>3



3.92/6<x-350.00>3



value of zero.

214

600g)

215


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +2.45<x-0.00>0 +3.43<x-600.00>0 - 5.89<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +2.45<x-0.00>1 +3.43<x-600.00>1 - 5.89<x-350.00>1


value of zero.


Force units = N



216


350.00>2


EI × Slope = +2.45/2<x-0.00>2 +3.43/2<x-600.00>2 - 121,603.13-

5.89/2<x-350.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-350.00>3



5.89/6<x-350.00>3



value of zero.

217

800g)

218


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-350.00>0


Shear = +3.27<x-0.00>0 +4.58<x-600.00>0 - 7.85<x-350.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-350.00>1


Moment = +3.27<x-0.00>1 +4.58<x-600.00>1 - 7.85<x-350.00>1


value of zero.


Force units = N



219


350.00>2


EI × Slope = +3.27/2<x-0.00>2 +4.58/2<x-600.00>2 - 162,137.50-

7.85/2<x-350.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-350.00>3



7.85/6<x-350.00>3



value of zero.

221

E)CD) 200g)@100mm

222


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +1.64<x-0.00>0 +0.33<x-600.00>0 - 1.96<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +1.64<x-0.00>1 +0.33<x-600.00>1 - 1.96<x-100.00>1


value of zero.


Force units = N



223


100.00>2


EI × Slope = +1.64/2<x-0.00>2 +0.33/2<x-600.00>2 - 29,975.00- 1.96/2<x-

100.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-100.00>3



1.96/6<x-100.00>3



value of zero.

224

200g)@200mm

225


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +1.31<x-0.00>0 +0.65<x-600.00>0 - 1.96<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +1.31<x-0.00>1 +0.65<x-600.00>1 - 1.96<x-200.00>1


value of zero.


Force units = N



226


200.00>2


EI × Slope = +1.31/2<x-0.00>2 +0.65/2<x-600.00>2 - 43,600.00- 1.96/2<x-

200.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-200.00>3



1.96/6<x-200.00>3



value of zero.

227

200g)@500mm

228


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.33<x-0.00>0 +1.64<x-600.00>0 - 1.96<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.33<x-0.00>1 +1.64<x-600.00>1 - 1.96<x-500.00>1


value of zero.


Force units = N



229


500.00>2


EI × Slope = +0.33/2<x-0.00>2 +1.64/2<x-600.00>2 - 19,075.00- 1.96/2<x-

500.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-500.00>3



1.96/6<x-500.00>3



value of zero.

230

400g)@100mm

231


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +3.27<x-0.00>0 +0.65<x-600.00>0 - 3.92<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +3.27<x-0.00>1 +0.65<x-600.00>1 - 3.92<x-100.00>1


value of zero.


Force units = N



232


100.00>2


EI × Slope = +3.27/2<x-0.00>2 +0.65/2<x-600.00>2 - 59,950.00- 3.92/2<x-

100.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-100.00>3



3.92/6<x-100.00>3



value of zero.

233

400g)@200mm

234


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +2.62<x-0.00>0 +1.31<x-600.00>0 - 3.92<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +2.62<x-0.00>1 +1.31<x-600.00>1 - 3.92<x-200.00>1


value of zero.


Force units = N



235


200.00>2


EI × Slope = +2.62/2<x-0.00>2 +1.31/2<x-600.00>2 - 87,200.00- 3.92/2<x-

200.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-200.00>3



3.92/6<x-200.00>3



value of zero.

236

400g)@500mm

237


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.65<x-0.00>0 +3.27<x-600.00>0 - 3.92<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.65<x-0.00>1 +3.27<x-600.00>1 - 3.92<x-500.00>1


value of zero.


Force units = N



238


500.00>2


EI × Slope = +0.65/2<x-0.00>2 +3.27/2<x-600.00>2 - 38,150.00- 3.92/2<x-

500.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-500.00>3



3.92/6<x-500.00>3



value of zero.

239

600g)@100mm

240


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +4.91<x-0.00>0 +0.98<x-600.00>0 - 5.89<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +4.91<x-0.00>1 +0.98<x-600.00>1 - 5.89<x-100.00>1


value of zero.


Force units = N



241


100.00>2


EI × Slope = +4.91/2<x-0.00>2 +0.98/2<x-600.00>2 - 89,925.00- 5.89/2<x-

100.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-100.00>3



5.89/6<x-100.00>3



value of zero.

242

600g)@200mm

243


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +3.92<x-0.00>0 +1.96<x-600.00>0 - 5.89<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +3.92<x-0.00>1 +1.96<x-600.00>1 - 5.89<x-200.00>1


value of zero.


Force units = N



244


200.00>2


EI × Slope = +3.92/2<x-0.00>2 +1.96/2<x-600.00>2 - 130,800.00-

5.89/2<x-200.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-200.00>3



5.89/6<x-200.00>3



value of zero.

245

600g)@500mm

246


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.98<x-0.00>0 +4.91<x-600.00>0 - 5.89<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.98<x-0.00>1 +4.91<x-600.00>1 - 5.89<x-500.00>1


value of zero.


Force units = N



247


500.00>2


EI × Slope = +0.98/2<x-0.00>2 +4.91/2<x-600.00>2 - 57,225.00- 5.89/2<x-

500.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-500.00>3



5.89/6<x-500.00>3



value of zero.

248

800g)@100mm

249


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +6.54<x-0.00>0 +1.31<x-600.00>0 - 7.85<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +6.54<x-0.00>1 +1.31<x-600.00>1 - 7.85<x-100.00>1


value of zero.


Force units = N



250


100.00>2


EI × Slope = +6.54/2<x-0.00>2 +1.31/2<x-600.00>2 - 119,900.00-

7.85/2<x-100.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-100.00>3



7.85/6<x-100.00>3



value of zero.

251

800g)@200mm

252


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +5.23<x-0.00>0 +2.62<x-600.00>0 - 7.85<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +5.23<x-0.00>1 +2.62<x-600.00>1 - 7.85<x-200.00>1


value of zero.


Force units = N



253


200.00>2


EI × Slope = +5.23/2<x-0.00>2 +2.62/2<x-600.00>2 - 174,400.00-

7.85/2<x-200.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-200.00>3



7.85/6<x-200.00>3



value of zero.

254

800g)@500mm

255


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +1.31<x-0.00>0 +6.54<x-600.00>0 - 7.85<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +1.31<x-0.00>1 +6.54<x-600.00>1 - 7.85<x-500.00>1


value of zero.


Force units = N



256


500.00>2


EI × Slope = +1.31/2<x-0.00>2 +6.54/2<x-600.00>2 - 76,300.00- 7.85/2<x-

500.00>2



value of zero.



EI = +11,249,997.63 N-mm²



P1/6<x-500.00>3



7.85/6<x-500.00>3



value of zero.

258

F)CL) 200g)

259


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +0.98<x-0.00>0 +0.98<x-500.00>0 - 1.96<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +0.98<x-0.00>1 +0.98<x-500.00>1 - 1.96<x-250.00>1


value of zero.


Force units = N



260


250.00>2


EI × Slope = +0.98/2<x-0.00>2 +0.98/2<x-500.00>2 - 30,656.25- 1.96/2<x-

250.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-250.00>3



1.96/6<x-250.00>3



value of zero.

261

400g)

262


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +1.96<x-0.00>0 +1.96<x-500.00>0 - 3.92<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +1.96<x-0.00>1 +1.96<x-500.00>1 - 3.92<x-250.00>1


value of zero.


Force units = N



263


250.00>2


EI × Slope = +1.96/2<x-0.00>2 +1.96/2<x-500.00>2 - 61,312.50- 3.92/2<x-

250.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-250.00>3



3.92/6<x-250.00>3



value of zero.

264

600g)

265


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +2.94<x-0.00>0 +2.94<x-500.00>0 - 5.89<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +2.94<x-0.00>1 +2.94<x-500.00>1 - 5.89<x-250.00>1


value of zero.


Force units = N



266


250.00>2


EI × Slope = +2.94/2<x-0.00>2 +2.94/2<x-500.00>2 - 91,968.75- 5.89/2<x-

250.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-250.00>3



5.89/6<x-250.00>3



value of zero.

267

800g)

268


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-250.00>0


Shear = +3.92<x-0.00>0 +3.92<x-500.00>0 - 7.85<x-250.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-250.00>1


Moment = +3.92<x-0.00>1 +3.92<x-500.00>1 - 7.85<x-250.00>1


value of zero.


Force units = N



269


250.00>2


EI × Slope = +3.92/2<x-0.00>2 +3.92/2<x-500.00>2 - 122,625.00-

7.85/2<x-250.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-250.00>3



7.85/6<x-250.00>3



value of zero.

271

F)CD) 200g)@100mm

272


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +1.57<x-0.00>0 +0.39<x-500.00>0 - 1.96<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +1.57<x-0.00>1 +0.39<x-500.00>1 - 1.96<x-100.00>1


value of zero.


Force units = N



273


100.00>2


EI × Slope = +1.57/2<x-0.00>2 +0.39/2<x-500.00>2 - 23,544.00- 1.96/2<x-

100.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-100.00>3



1.96/6<x-100.00>3



value of zero.

274

200g)@200mm

275


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +1.18<x-0.00>0 +0.78<x-500.00>0 - 1.96<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +1.18<x-0.00>1 +0.78<x-500.00>1 - 1.96<x-200.00>1


value of zero.


Force units = N



276


200.00>2


EI × Slope = +1.18/2<x-0.00>2 +0.78/2<x-500.00>2 - 31,392.00- 1.96/2<x-

200.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-200.00>3



1.96/6<x-200.00>3



value of zero.

277

200g)@400mm

278


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +0.39<x-0.00>0 +1.57<x-500.00>0 - 1.96<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +0.39<x-0.00>1 +1.57<x-500.00>1 - 1.96<x-400.00>1


value of zero.


Force units = N



279


400.00>2


EI × Slope = +0.39/2<x-0.00>2 +1.57/2<x-500.00>2 - 15,696.00- 1.96/2<x-

400.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-400.00>3



1.96/6<x-400.00>3



value of zero.

280

400g)@100mm

281


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +3.14<x-0.00>0 +0.78<x-500.00>0 - 3.92<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +3.14<x-0.00>1 +0.78<x-500.00>1 - 3.92<x-100.00>1


value of zero.


Force units = N



282


100.00>2


EI × Slope = +3.14/2<x-0.00>2 +0.78/2<x-500.00>2 - 47,088.00- 3.92/2<x-

100.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-100.00>3



3.92/6<x-100.00>3



value of zero.

283

400g)@200mm

284


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +2.35<x-0.00>0 +1.57<x-500.00>0 - 3.92<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +2.35<x-0.00>1 +1.57<x-500.00>1 - 3.92<x-200.00>1


value of zero.


Force units = N



285


200.00>2


EI × Slope = +2.35/2<x-0.00>2 +1.57/2<x-500.00>2 - 62,784.00- 3.92/2<x-

200.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-200.00>3



3.92/6<x-200.00>3



value of zero.

286

400g)@400mm

287


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +0.78<x-0.00>0 +3.14<x-500.00>0 - 3.92<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +0.78<x-0.00>1 +3.14<x-500.00>1 - 3.92<x-400.00>1


value of zero.


Force units = N



288


400.00>2


EI × Slope = +0.78/2<x-0.00>2 +3.14/2<x-500.00>2 - 31,392.00- 3.92/2<x-

400.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-400.00>3



3.92/6<x-400.00>3



value of zero.

289

600g)@100mm

290


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +4.71<x-0.00>0 +1.18<x-500.00>0 - 5.89<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +4.71<x-0.00>1 +1.18<x-500.00>1 - 5.89<x-100.00>1


value of zero.


Force units = N



291


100.00>2


EI × Slope = +4.71/2<x-0.00>2 +1.18/2<x-500.00>2 - 70,632.00- 5.89/2<x-

100.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-100.00>3



5.89/6<x-100.00>3



value of zero.

292

600g)@200mm

293


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +3.53<x-0.00>0 +2.35<x-500.00>0 - 5.89<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +3.53<x-0.00>1 +2.35<x-500.00>1 - 5.89<x-200.00>1


value of zero.


Force units = N



294


200.00>2


EI × Slope = +3.53/2<x-0.00>2 +2.35/2<x-500.00>2 - 94,176.00- 5.89/2<x-

200.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-200.00>3



5.89/6<x-200.00>3



value of zero.

295

600g)@400mm

296


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +1.18<x-0.00>0 +4.71<x-500.00>0 - 5.89<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +1.18<x-0.00>1 +4.71<x-500.00>1 - 5.89<x-400.00>1


value of zero.


Force units = N



297


400.00>2


EI × Slope = +1.18/2<x-0.00>2 +4.71/2<x-500.00>2 - 47,088.00- 5.89/2<x-

400.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-400.00>3



5.89/6<x-400.00>3



value of zero.

298

800g)@100mm

299


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-100.00>0


Shear = +6.28<x-0.00>0 +1.57<x-500.00>0 - 7.85<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-100.00>1


Moment = +6.28<x-0.00>1 +1.57<x-500.00>1 - 7.85<x-100.00>1


value of zero.


Force units = N



300


100.00>2


EI × Slope = +6.28/2<x-0.00>2 +1.57/2<x-500.00>2 - 94,176.00- 7.85/2<x-

100.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-100.00>3



7.85/6<x-100.00>3



value of zero.

301

800g)@200mm

302


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-200.00>0


Shear = +4.71<x-0.00>0 +3.14<x-500.00>0 - 7.85<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-200.00>1


Moment = +4.71<x-0.00>1 +3.14<x-500.00>1 - 7.85<x-200.00>1


value of zero.


Force units = N



303


200.00>2


EI × Slope = +4.71/2<x-0.00>2 +3.14/2<x-500.00>2 - 125,568.00-

7.85/2<x-200.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-200.00>3



7.85/6<x-200.00>3



value of zero.

304

800g)@400mm

305


Length units = mm



Shear = Ay<x-0.00>0 +By<x-500.00>0 - P1<x-400.00>0


Shear = +1.57<x-0.00>0 +6.28<x-500.00>0 - 7.85<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-500.00>1 - P1<x-400.00>1


Moment = +1.57<x-0.00>1 +6.28<x-500.00>1 - 7.85<x-400.00>1


value of zero.


Force units = N



306


400.00>2


EI × Slope = +1.57/2<x-0.00>2 +6.28/2<x-500.00>2 - 62,784.00- 7.85/2<x-

400.00>2



value of zero.



EI = +26,666,661.05 N-mm²



P1/6<x-400.00>3



7.85/6<x-400.00>3



value of zero.

309

In this part we want to test the Maxwell theorem.

This section is in four parts as mentioned as below with a brass (C83400,

E=101 GPa, 25*4*600 mm) beam

PART1) Load: 200g @ 100mm, Deflectometer @ 400mm




310

PART1)

- Brass (C83400, E=101 GPa, 25*4*600 mm)

311


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-100.00>0


Shear = +1.64<x-0.00>0 +0.33<x-600.00>0 - 1.96<x-100.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-100.00>1


Moment = +1.64<x-0.00>1 +0.33<x-600.00>1 - 1.96<x-100.00>1


value of zero.


Force units = N



312


100.00>2


EI × Slope = +1.64/2<x-0.00>2 +0.33/2<x-600.00>2 - 29,975.00- 1.96/2<x-

100.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-100.00>3



1.96/6<x-100.00>3



value of zero.

313

PART2)

- Brass (C83400, E=101 GPa, 25*4*600 mm)

314


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-400.00>0


Shear = +0.65<x-0.00>0 +1.31<x-600.00>0 - 1.96<x-400.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-400.00>1


Moment = +0.65<x-0.00>1 +1.31<x-600.00>1 - 1.96<x-400.00>1


value of zero.


Force units = N



315


400.00>2


EI × Slope = +0.65/2<x-0.00>2 +1.31/2<x-600.00>2 - 34,880.00- 1.96/2<x-

400.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-400.00>3



1.96/6<x-400.00>3



value of zero.

316

PART3)

- Brass (C83400, E=101 GPa, 25*4*600 mm)

317


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-200.00>0


Shear = +2.62<x-0.00>0 +1.31<x-600.00>0 - 3.92<x-200.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-200.00>1


Moment = +2.62<x-0.00>1 +1.31<x-600.00>1 - 3.92<x-200.00>1


value of zero.


Force units = N



318


200.00>2


EI × Slope = +2.62/2<x-0.00>2 +1.31/2<x-600.00>2 - 87,200.00- 3.92/2<x-

200.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-200.00>3



3.92/6<x-200.00>3



value of zero.

319

PART4)

- Brass (C83400, E=101 GPa, 25*4*600 mm)

320


Length units = mm



Shear = Ay<x-0.00>0 +By<x-600.00>0 - P1<x-500.00>0


Shear = +0.65<x-0.00>0 +3.27<x-600.00>0 - 3.92<x-500.00>0


value of zero.




Moment = Ay<x-0.00>1 +By<x-600.00>1 - P1<x-500.00>1


Moment = +0.65<x-0.00>1 +3.27<x-600.00>1 - 3.92<x-500.00>1


value of zero.


Force units = N



321


500.00>2


EI × Slope = +0.65/2<x-0.00>2 +3.27/2<x-600.00>2 - 38,150.00- 3.92/2<x-

500.00>2



value of zero.



EI = +13,466,663.83 N-mm²



P1/6<x-500.00>3



3.92/6<x-500.00>3



value of zero.

322

Results and questions:

It’s better to bring back the table of each experiment again to have a better

explanation…

Here we for example bring the experiments as:

ACL

And actually we must have some error considerations such as: default error

that comes from the measuring tool and system, error of default deflections of

beam, the equation error, vision error and errors of errors.

Material A

Constant Load

Location experiment

323 ACL)

As we see, the deviation of errors seems to be at same range; except the first

which is 27.15% that it could be of vision error.

Another point that should be mentioned is that first two steps of the

experiment are as the same range like the second pair. That could be of

changing the location of beam on the experiment set.

ACD)

In this state we see that the first error is proportionally large that could be of

vibration of experiment set. As we see in the next parts of experiment, the

ranges of errors are approximately the same that are default errors.

324

BCL)

In first stage of this table we could have vibration errors as mentioned

before.

In next stages it seems an approximately constant slope for errors that could

be of default deflection of beam.

BCD)

Like last experiments, as we see here we have big errors in first part, too;

which its reason mentioned.

325

Low altitude of errors in next stages shows that the beam is not deflected

and large part of error is of the measuring tool and the experiment set.

CCL)

At two parts of experiment, which are part 2 & 3, the ranges of errors are

approximately the same, which are default errors.

In part 4, we see that the altitudes of errors are low, which it could be the

error of error because of increasing the force.

CCD)

326

Like one of the results that brought before, we see a constant slope in errors

that comes from the primary deflection in beam.

DCL)

As we see, in the first experiment, there are some errors that seem to be

larger than the next experiments proportionally. This could because of set

vibrations and deflectometers. Actually the deflectometers have a default error

because of their structure and locations.

DCD)

327

As it was pointed before, the first experiment of each stage has large error

because of some problems that mentioned before. Here we see that error as

7.19%.

The others could because of equations, human vision and default

deflectometer’s error.

ECL)

Here as we see the error altitudes, it seems that the beam had primary

deflection.

Also the range of error altitudes shows us that we had vision errors in this

experiment.

328

ECD)

Except the first part of experiment that has large altitude of errors, which

could be of set vibrations; other error altitude parts are acceptable.

FCL)

In this experiment we have primary deflection in beam, too. But the 19.49%

error, which seems in first part of experiment, could be a vision error.

329

FCD)

Like other first step errors, it seems in this experiment too. Also we see the

proportionally large altitude of error at 200mm in all stages; which could be of

primary deflection.

Maxwell theorem: - Brass (C83400, E=101 GPa, 25*4*600 mm)

Such error altitudes are because of human vision.

Another point that should be mentioned here is that as we see for example

second experiment, both theoretic and practical values are the same, but we

have the 0.36% error value. This is because of fixing digits in spreadsheet

software (Excel).

330

At last:

Here we bring back the papers that had written at laboratory which signed

by instructor.

Report (Determined Beams & Maxwell Theorem)

Documents

Transcript of Report (Determined Beams & Maxwell Theorem)