Diagram of Beam – with Neutral Axis
SF/BM Diagrams
Data Graphs
Graph 1 - Strai& 's( Be&)i&g Mome&t %0 $0 #0 50
Be&)i&g Mome&t +Nm,
Gauge 1
*i&ear +Gauge 1,
Gauge
*i&ear +Gauge ,
Gauge !
*i&ear +Gauge !,
Gauge "
*i&ear +Gauge ",
"0
Gauge 5
*i&ear +Gauge 5,
!0
Gauge #
*i&ear +Gauge #,
0
Gauge $
*i&ear +Gauge $,
Gauge %
*i&ear +Gauge %,
Gauge
*i&ear +Gauge ,
10 -500
0
0
500
Strai& +.,
Graph - Strai& 's( Nomi&al 2erti3al 4ositio& of Strai& "0 f+x, 0(0 f+x,#x 0(0%x 5(# f+x, 0(1 f+x, 5(" 1x 0(1$x f+x, 5( 5($$ 0(5x 5(5 !0 0
Nomi&al 2erti3al 4ositio& +mm,
10
-500
-"00
-!00
-00
-100
0
0
100
00
Strai& +., %($5Nm
*i&ear +%($5Nm,
#(5Nm
*i&ear +#(5Nm,
"!($5Nm
*i&ear +"!($5Nm,
#1(5Nm
*i&ear +#1(5Nm,
$%($5Nm
*i&ear +$%($5Nm,
al3ulatio&s ¿ data tables , M max=78.75 Nm
Y − AxisCentroid ( !xperimentally )
Y − AxisCentroid ( Theoretically ) y´ =
¿
¿
Σ A i y i
y =0.4987 x + 25.496 … … … … … … ( 1)
Σ A i
( 6.4 × 31.7 ) ( 15.85 ) + ( 38.1 × 6.4 ) ( 34.9 ) y =0.0606 x + 25.956 … … … … … … ( 2 ) ( 6.4 × 31.7 ) + ( 38.1 × 6.4 ) 0.4381 x =0.460
11725.664 446.72
¿ 26.248 … mm ¿ 26.25 mm (2 dp ) ¿ the top
¿ Axis Theorem 4
I ( mm
Shape Top
31.7
3
)
A ( mm
× 6.4
12 6.4
Base
3
× 38.1 12
I xx= I + A d
2
2
2
d i ( mm
)
31.7 × 6.4
6.4 × 38.1
2
)
Ad i ( mm
108.16
74.8225
4
)
I xx ( mm
21943.5008
18244.7184
4
)
I xx ( m
−9
38.93 × 10
19077.0256
19.08 × 10
−9
¿ 38.93 × 10−9 + 19.08 × 10−9 ¿ 58.01 × 10−9 m4
Bending Stress My = I !xperimentally
$here ´ y =26.25 mm
=
78.75 Nm × 26.25 × 10 9
4
−3
$here ´ y =26.02 mm
m
=
)
38932.84107
2
Theoretically
4
−3 78.75 Nm × 26.02 × 10 m 9
4
%ercentage !rror &!rror =
theo' − exp ' theo'
¿
35.635
× 100
−35.323
35.635
× 100
¿ 0.876 ( 3 dp )
Dis3ussio& 6& this experime&t7 the relatio&ship 8etwee& the 8e&)i&g mome&t a&) the strai& was fou&) to 8e 3losel9 )epe&)e&t o& the positio&i&g of the gauge rea)i&g i& terms of the &eutral axis( 6f the gauge meter was a8o'e the &eutral axis7 the strai& ha) a &egati'e tre&)( :& other ha&)7 if the gauge meter was 8elow the &eutral axis7 the strai& ha) a positi'e tre&)( ;his is 8e3ause the top part of the 8ar u&)erwe&t a 3ompressi'e for3e7 whi3h pro)u3es a &egati'e strai&( owe'er7 experime&tall9 this was &ot the 3ase( ;here were a few )is3repa&3ies 8etwee& these 3lose gauge rea)i&gs( ;he 8ar ge&erall9 3o&tai&s impurities whi3h 3auses the i&ter&al a&) applie) for3es to &ot 8e )istri8ute) as e=uall9 as expe3te) from the theoreti3al 3al3ulatio&s( Also7 real life appli3atio&s are &e'er as perfe3tl9 shape) as expe3te) )ue to the u&realisti3 i)eal measureme&ts i& these tools a&) ma3hi&es( >e&3e7 the &o&-homoge&ous properties of real life appli3atio&s 3oul) also )istort the )istri8utio& of for3es a&) the 8e&)i&g mome&ts )uri&g the experime&ts( 6& Graph 7 all the li&es of 8est ?t 3ross at a mutual poi&t7 where the &eutral axis was expe3te) to 8e from the top( ;he experime&tal 'alue of the &eutral axis was #(0 mm7 a&) the theoreti3al 'alue was #(5 mm(
;his pro)u3e) a& error of 0(%$#@7 whi3h mea&s that the experime&t was fairl9 a33urate(
o&3lusio& ;his experime&t measure) the &eutral axis from the top as #(0 mm7 where the theoreti3al 'alue was 3al3ulate) to 8e #(5 mm – with a& error of 0(%$#@( Also7 this experime&t was a8le to 3ome to the 3o&3lusio& that the 3loser a poi&t is to the &eutral axis7 the strai&/stress experie&3e) woul) 8e a lot less tha& a poi&t further awa9(
