meen20040 mechanics of solids i deflection of beams in bending name ho
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MEEN20040 Mechanics of Solids I
Deflection of beams in Bending
Name: HOOR MM M ALMHANA Student Number: 21209980
Introduction
The deflection in beams in bending depends on
• Young's modulus E
Load applied
•
Length of the beam
•
Cross sectional geometry, 2nd moment of area I
Date:
29/02/2024
Distribution of the applied load
For a beam in three point bending the deflection is given by the formula
FL³
ဝ် -
where
48.E.I
S is the deflection of the beam,
F is the applied force
L is the length of the beam
E is Young's modulus
I is the 2nd moment of area
bh³
For a rectangular cross section this is given by I
12
b: beam width, h: beam thickness
12.FL³
8 =
48..b.h³.E
b
d =
FL³
4..b.h³.E
δ
F
# 1. Deflection depending on applied force
Use Aluminium bar. Cross section b× h = 20 × 5mm.
Length = 50cm
Load body with weight 5, 10, 15 and 20 N
Measure deflection at each load
Weight of load body [N]
Deflection [mm]
δαμ
5 10 15 20
0.86 1.68 2.55 2.78
F = m.g
Plot deflection versus mass and comment on the influence of the applied load on the
deflection of the beam. This is acceptable as m is linearly related to applied load
2 deflection
(mm)_
2. Deflection depending on bar length L
Use Aluminium bars. Cross section b× h = 20 × 4 mm
Length of bars is 20, 30, 40 and 50 cm.
Apply 10 N load for each bar and measure deflection.
Length [cm]
20
30
40
δαι
50
Deflection [mm] 0.22 0.79 1.97 5.74
L³ in cm³
8000
27000 64000 125000
Plot deflection versus Ls and comment on the influence of the length on the deflection of
the beam
Linear Relationship
3
L³ (m³)
3 3. Deflection depending on profile width b
Use Aluminium bars. Thickness is 5 mm. Length 50 cm
Width of bars varies as 10, 15, 20, 25 mm. Length = 50 cm.
Apply 10 N load for each bar and measure the deflection.
8 x 1½
b
Profile bxh [mm]
10 × 5
Deflection [mm]
3.7
15 × 5
20 x 5*
2.33 1.68
25 × 5
1.43
1/b [1/mm]
0.1
0.0666 0.05
0.04
Plot deflection versus 1/b and comment on the influence of the profile width on the
deflection of the beam 4. Deflection depending on profile thickness h
Use Aluminium bars. Width is 20 mm. Length is 50 cm
Height: 3, 4, 5, 6, and 8 mm.
Apply 10 N load and measure, the deflection for each bar
-13
Ꮵ
Profile
Deflection [mm]
1/h3 [1/mm³]
20 × 3 20 × 4*
7.25 3.74
20 × 5*
20 × 6
20 × 10
1.68
1-15
0-2
0.037
0.0145
0.008
0.00487 0.00203
0.001
Plot deflection versus 1/h³ and comment on the influence of the thickness on the
deflection of the beam
5/n Name:
MEEN20040 Mechanics of Solids I
Deflection of beams in Bending
Introduction
The deflection in beams in bending depends on
• Young's modulus E
Load applied
• Length of the beam
Student Number:
Date:
•
•
Cross sectional geometry, 2nd moment of area I
Distribution of the applied load
For a beam in three point bending the deflection is given by the formula
8 =
FL³
48.E.I
where
S is the deflection of the beam,
F is the applied force
L is the length of the beam
E is Young's modulus
I is the 2nd moment of area
For a rectangular cross section this is given by I
b: beam width, h: beam thickness
12.FL³
δε
48..b.h³.E
h
FL³
δ
4..b.h³.E
b
1
=
bh³
12
δ
F 1. Deflection depending on applied force
Use Aluminium bar. Cross section b × h = 20 × 5mm.
Length = 50cm
Load body with weight 5, 10, 15 and 20 N
Measure deflection at each load
δα F
F = m.g
Weight of load body [N]
5
10
15 20
Deflection [mm]
Plot deflection versus mass and comment on the influence of the applied load on the
deflection of the beam. This is acceptable as m is linearly related to applied load
2 2. Deflection depending on bar length L
Use Aluminium bars. Cross section b× h = 20 × 4 mm
Length of bars is 20, 30, 40 and 50 cm.
Apply 10 N load for each bar and measure deflection.
Length [cm]
Deflection [mm]
20
30
L³ in cm³
8000
δα
40
50
27000 64000 125000
Plot deflection versus L³ and comment on the influence of the length on the deflection of
the beam
3 3. Deflection depending on profile width b
Use Aluminium bars. Thickness is 5 mm. Length 50 cm
Width of bars varies as 10, 15, 20, 25 mm. Length = 50 cm.
Apply 10 N load for each bar and measure the deflection.
Profile b × h [mm] 10×5 15 × 5 20 × 5* 25 × 5
Deflection [mm]
1/b [1/mm]
0.1
0.0666 0.05
0.04
1
δα
b
Plot deflection versus 1/b and comment on the influence of the profile width on the
deflection of the beam
4 4. Deflection depending on profile thickness h
Use Aluminium bars. Width is 20 mm. Length is 50 cm
Height: 3, 4, 5, 6, and 8 mm.
Apply 10 N load and measure the deflection for each bar
Profile
1
δα
h³
20 × 3 20 × 4* 20 × 5* 20 × 6
20 × 10
Deflection [mm]
1/h³ [1/mm³]
0.037 0.0145 0.008
0.00487 0.00203
Plot deflection versus 1/h³ and comment on the influence of the thickness on the
deflection of the beam
5