Shear Center of Open Sections (Channel)

SHEAR CENTER OF OPEN SECTIONS (CHANNEL) AIM:

Shear center of an open section determination. THEORY:

For any unsymmetrical section there exists a point at which any vertical force force does not produce produce a twist twist of that section section.. This This point is known known as shear  shear  center. The location of this shear center is important in the design of beams of  open sections when they should bend without twisting, as they are weak in channel el section with its web vertical has a resisti resisting ng torsi torsion. on. A thin thin walled walled chann

horizon horizontal tal axis axis of symmet symmetry ry and the shear center center lies lies on it. it. The The aim of the experiment is to determine its location on this axis if the applied shear to the tip section is vertical i.e. along the direction of one of the principal axes of the section! and passes through the shear center tip, all other sections of the beam do not twist. APPARATUS APPARATUS REQUIRED: REQUI RED: •

A thin uniform cantilever beam of channel section as shown in the figure. At the free end extension pieces are attached on either side of the web to facilitate vertical loading.

•

Two dial gauges are mounted firmly on this section, a known distance apart, over over the top flange. This enables enables the determinati determination on of the twist, if  any, experienced by the section.

•

A steel support structure to mount the channel section as cantilever.

•

Two Two loading hooks hook s each weighing about ".#$g.

#

PROCEDURE:

#. %ount two dial gauges on the flange at a known distance apart at the free end of the beam see fig!. Set the dial gauge readings to zero. &. 'lace a total of say 1.2 !l"#$a%&  load at A loading hook and &!' l"a  pieces will make up this value!. (ote the dial gauge readings (H""& al&" e!#h a 1** #$a%& each). A)side dial gauge rotate in anticlockwise

direction. *)side dial gauge rotate in clockwise direction. (ote down the dial gauge reading. +. (ow remove one load piece from the hook at A and place in hook at *. This means that the total vertical load on this section remains #. kilogram. -ecord the dial gauge readings. . Transfer carefully all the load pieces to * one by one. (oting each time the dial gauge readings. This procedure ensures that while the magnitude of the resultant vertical force remains the same its line of action shifts by a known amount along A* every time a load piece is shifted. alculate the distance /e0 see fig! of the line of action from the web thus1 A* 2a)2 b! e3

&2v

4. For every load case calculate the algebraic difference between the dial gauge is u)v! readings as the measure of the angle of twist θ suffered by the section. 5. 6ial gauge to be mounted as near to the web as possible. 7. 'lot θ against e and obtain the meeting point of the curve a straight line in this case! with the e)axis i.e., θ the twist of the section is zero for this location of the resultant vertical load!. This determines the shear center.

&

Though a nominal value of #.& kilograms for the total load is suggested it can be less.

8n that event the number of readings taken will reduce

 proportionately.

READIN+S AND CALCULATIONS

TA,LE

6imensions of the beam and the section1 9ength of the beam 9!

1

4"cm

:eight of the web h!

1

#"cm

2idth of the flange b!

1

4cm

Thickness of the sheet t!

1

#.5mm

6istance between the two hook stations A*!

1

+"cm

The"$e-!cal l"ca-!"n " -he &hea$ cen-e$ (e): / 0  345 (h)6

;ertical load 2v 3 2a<2 b!

S. (o.

2a

2 b

d#

d&

d#)d&

e

# & +  4 5 7 'lot e versus d#)d&! curve and determine where this meets the e axis and locate the shear center.

+

PRECAUTIONS

#. For the section supplied there are limits on the maximum value of loads to obtain acceptable experimental results. *eyond these the section could undergo excessive permanent deformation and damage the beam forever. 6o not therefore exceed the suggested values for the loads. &. The dial gauges must be mounted firmly. =very time before taking the readings tap the set up not the gauges! gently several times until the reading pointers on the gauges settle down and do not shift any further. This shift happens due to both backlash and slippages at the points of  contact between the dial gauges and the sheet surfaces and can induce errors if not taken care of. -epeat the experiments with identical settings several times to ensure consistency in the readings.

2eights given &"" gm ) 5



TA,LE OF READIN+S

e 3 A* 2a)2 b!> &?2v! 2v32a<2 b A* 3+"" mm

READINGS AND CALCULATIONS FOR JAIN(CHANNEL) Sl.N o

Wa in Kg

Wb in Kg

1

1.3

0.1

102

501

-399

1.4

2

1.1

0.3

167

431

-264

1.4

3 4

0.9 0.7

0.5 0.7

237 311

356 282

-119 29

1.4 1.4

5

0.5

0.9

378

212

166

1.4

6

0.3

1.1

452

140

312

1.4

7

0.1

1.3

528

66

462

1.4

ethe

eexp

d1 in mm

3

+b ))))))))) 3 5< h>b!

3

A* 2a)2 b! )))))))))))))))) &2v

d2 in mm

+×4 ))))))))))) 5< #">4!

(d1-d2) mm

3

in

Wv in Kg

e in mm 128.57 14 85.714 29 42.857 14 0 42.857 1 85.714 3 128.57 1

1.789c%

2here A* 3 length of the centre to centre hook distance. From centre to centre of load

3

+" #.+)".#! ))))))))))))))) &×#.

3

12.74 cm.

6raw the graph

4

-ead point → e → distance from " positions in the graph.  eexp 3 from graph! eth is #.@74

+RAPH (9B F- CD86A(=!

C"ncl&!"n: ethEeexp and nearer to the value. The difference due to error may be noting down the readings. This shift happens due to both backlash and slippages at the points of contact  between the dial gauges and the sheet surfaces and can induce errors if not taken care of. -epeat the experiments with identical settings several times to ensure consistency in the readings.

5