plastic bending of steel

8/12/2019 Plastic Bending of steel

1/12

Plastic Bending of Steel

Page | 1

Title of Experiment: Plastic Bending of Steel

Aim of Experiment: To compare plastic bending moment from theoretical and experiment of

steel sections under load for three different support arrangements.

Parameters:

Yield stress of Steel: 275N/mm2(Structural AST!A"#$

Young%s odulus& 2'' x '"N/mm2(Structural AST!A"#$

Support Arrangement 1: Simply Supported Steel Beam with Point load mid-span

Beam geometric properties: )ength * +#'mm, b * 2-.+#mm, d * 5.-mm

istance bet0een supports * 5'mm

Second oment of Area (1$ *

..

434.19

285 285

?

?

Mp Mp

?

A B

C

A B

C

D

D

Fig.1: showing plastic bending moment and plastic moment mechanism.


2/12


Page | 2

inges are formed at 3 0hich is the position 0here the load acts directl4 on, moments

formed at that position is the plastic moment. The deformation from point load mid!span

is

,

66. (A$ !"#$, %&&%'

Soling to get pfrom the plastic mechanism diagram aboe

(ADC* ()*+(Similar triangles$

Assuming the )ength of the steel bar as ),

A8 * ), A * )/2, 3 *

9rom :irtual ;or< Theorem

;or< done outside b4 force and displacement * ;or< done inside b4 plastic hinge

9orce x distance * oment x rotation

- / -666666666666 ($

;here

"#666666666666. (2$

;here the alue of is er4 small thus tan

=>uation ($ then becomes

0

- / -6666666666666666 ("$

0

%-666666666666666666666. (-$

4-66666666666666666666 (5$

iide both sides of the e>uation b4

4-666666666666666666666... (#$

-66666666666666666666666 (7$

Soling theoreticall4 for p

oment * Yield stress ? Section odulus

- -

;here - %2&and - 5

. .5

%19.3&6

- %2&

%19.33 247%2

@utting alue of pinto e>uation # to get @


3/12


Page | 3

29& 4 247%2

381.8

@utting alue of @ into e>uation A to get the displacement at that theoretical load

381.8 29&6

4 7 % & & 1 &6 434.19 17.33

Soling for p from aximum )oad from experiment (ax. )oad * "#-N and %4.422$

-

4

34 29&

4 239&

p using experimental alue * 5"#'Nmm, p(theoreticall4$ * 5-+25Nmm

@ercentage difference bet0een the t0o alues is sho0n belo0

: ;#? 247%2 @ 239&239&

1&& %.1%:

Fig. 2: showing load-displacement graphs from experimental and theoretical methods

Experimental

theoretical


4/12


Page | 4

Support Arrangement 2: Propped antile!er Steel Beam

Beam geometric properties: )ength * +#'mm, b * 2-.+'mm, d * 5.-mm



.A.

433.14

285 285

Mp Mp

A B

C

A B

C

D

D

d

P

Mp

Fig.3; showing plastic bending moment and plastic moment mechanism diagrams for a propped cantilever steel

beam

inges are formed at point A (0here there is a fixed support$ and @oint 3 0here the load

acts directl4 on

eflection at mid!span due to )oad 'B

B 66666666(A$ ()eet Bang, 2''2$.

;hile the @oint )oad, B

B 666666666666666.....(8$

)et%s assume that the steel beam length e>uals )


5/12


Page | 5

Soling for p for the propped cantileer beam aboe using the irtual 0or< method as

done preiousl4

- / - / -666666666666 ($

;here

"#C666666666666. (2$



0

- / - / -66666666666.. ("$

0

3-666666666666666666666. (-$

-66666666666666666666 (5$


-666666666666666666666... (#$

-66666666666666666666666 (7$



- -

;here - %2&and - 5

.A .5

%17.86

- %2&

%17.83 249&


29& 249&

22.18


8 22.18 29&6

87 %&& 1&6 433.14 1%.&%

Soling for p from aximum )oad from experiment (ax. )oad * 5'N at 27.81%$

-

29& 29&

27&1

p using experimental alue * 5+'#Nmm, p(theoreticall4$ * 5-#'Nmm



6/12


Page | 6

: ;#? 27&18 @ 249&

249& 1&& .&7:

Fig 3: showing graph of experimental and theoretical vales for load vs. displacement for a propped cantilever

steel beam.

Experiment

theoretical


7/12


Page | 7

Support Arrangement ": Steel #eam with point load at mid-span with ends fully

fixed

Beam geometric properties: )ength * +#'mm, b * 25.'mm, d * #.'+mm



.A.A

48&.11

285 285

?

?

Mp Mp

?

A B

C

D

Mp Mp

?d

Fig.5: showing plastic moment bending diagram and mechanism for a fully fixed Steel beam


eflection of the full4 fixed beam

inges are formed at point A, 8 (0here there are fixed supports$ and @oint 3 0here theload acts directl4 on


8/12


Page | 8

eflection at mid!span due to )oad '

666666 (A$ ()eet Bang, 2''2$

;hile the @oint )oad,

66666666666666 (8$


Soling for p for the propped cantileer beam aboe using the irtual 0or< method as

done preiousl4

- / - / - / -666666666666 ($

;here

"#666666666666. (2$



0

- / - / - / -66666666666.. ("$

0

4-666666666666666666666. (-$

7-66666666666666666666 (5$


7-666666666666666666666... (#$

-66666666666666666666666 (7$



- -

;here - %2&and - 5

.A .A5

%31.96

- %2&

%31.93 2899&


29& 7 249&

841.2


841.2 29&

6

19% %&& 1&6 48&.11 7.44


9/12


Page | 9

Soling for p from aximum )oad from experiment (ax. )oad * '2+N at 9.431$

-

7

1&%7 29&

7 87212

p using experimental alue * 7+55Nmm, p(theoreticall4$ * 57'Nmm


: ;#? 87212 @ 2899&

2899& 1&& 32.4&:

Fig !: "raph showing plastic moments for fll# fixed steel beam from experimental and theoretical methods

0

200

400

600

800

1000

1200

0.000 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 90.000

Experimental

theoretical


10/12


Page | 10

$iscussion

@lastic design anal4sis is premised on the assumption that an ultimate load is reached

before secondar4 effects such as member instabilit4 causes member failure( 3laruired number of plastic hinges that are needed to transform the structure into a

mechanism(geometricall4 unstable$ must be in place and further load at this point 0ill

cause collapse.

1t is expected that alues from experiments should corroborate alues from theor4

because experiments are used to alidate h4pothesis to become theories. 8ased on this

0e can relate it to our test, for the stcondition, 0hich is a simpl4 supported 0hich is a

staticall4 determinate beam, re>uires the formation of Dust one plastic hinge (0hich in

this case is formed at the point of loading$ 0hich should occur 0hen the moment at mid!

span reaches the plastic moment. The oment of plasticit4 gotten from experimental is

less than theoretical alues b4 2E, this could hae been as a result of the ):T not being

at the centre bet0een supports thus not tauiring more than one plastic

hinge to form a mechanism, the plastic moment from theoretical is #.'+E but test cannot

be relied upon because the ):T moed out of the steel beam 0hile force 0as still loaded

on the steel member mauiring larger

load.

%ndustry Applications of Plastic $esign & Analysis

1t is used in the anal4sis and design of staticall4 determinate framed structures 1t is used in the design of steel structures 1t brings cost!saings due to lighter members from anal4sis and design compared

to the elastic method


11/12


Page | 11

esigning a member b4 plastic anal4sis gies the member a resere momentcapacit4 0hen the member reaches 4ield capacit4 as signified b4 the shape factor

of the member

;ith plastic anal4sis a structure can be designed to form a predetermined 4ieldmechanism at ultimate load leel to create possible scenarios 0here the response

of the member to such situations are


12/12


Page | 12

plastic bending of steel

Documents