Department of Mechanical and Civil Engineering EN200: Applied Mechanics Lab. Bending of Thin Curved...

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Department of Mechanical and Civil Engineering EN200: Applied Mechanics Lab. Bending of Thin Curved Beam OBJECTIVES To estimate the theoretical end displacements of three arrangements of bar and to compare these values with actual measurements. APPARATUS Norwood curved bar apparatus. Weights, dial gauges, bridge. Curved beam dimensions: B*D : 20mm * 5mm Radii : 150 mm E = 200 GPa THEORY If a curved beam is loaded at one end, the beam, apart from being strained, will deform and the deflections can be measured by two components ?V (vertical) and ?H (horizontal). Using Castigliano’s theorem, the deflections can be expressed by equations that involve load (W), dimension of the beam(R), material(E)and cross-sectio
	
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NORTHUMBRIA UNIVERSITY
Department of Mechanical and Civil Engineering
EN200: Applied Mechanics Lab.
 Bending of Thin Curved Beam
 
OBJECTIVES 
To estimate the theoretical end displacements of three arrangements of bar and to 
compare these values with actual measurements. 
 
APPARATUS 
Norwood curved bar apparatus. Weights, dial gauges, bridge. 
Curved beam dimensions: 
 
B*D : 20mm * 5mm 
Radii : 150 mm 
E = 200 GPa 
THEORY 
If a curved beam is loaded at one end, the beam, apart from being strained, will deform 
and the deflections can be measured by two components ? (vertical) and ? (horizontal). 
V H
Using Castigliano’s theorem, the deflections can be expressed by equations that involve 
load (W), dimension of the beam(R), material(E)and cross-sectional properties (I) of the 
beam.  
 
The mild steel curved beams that would be tested in this experiment as well as the 
corresponding vertical and horizontal displacements are shown below.  
 
(Beam 1)                         XXXXXXXXXXBeam 2)                    XXXXXXXXXXBeam 3)

3 3 3
WR 2WR WR
d? …………...(1a)  d? ….(2a)      d? …...(3a) 
H H H
4EI EI 2EI
 
3 3 3
2WR? 1?WR WpR
 ..(1b XXXXXXXXXX2b)      … (3b) 
d? (? )d?d?
V V V
EI 8? 2EI 4EI
 
(Safe load: 80N)   (Safe load: 60N)     XXXXXXXXXXSafe load: 80N)           
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RISK ASSESSMENT  
Hazard:  
Impact from falling objects (weights and hangers) 
Control Measures Required:  
Students to strictly follow instructions and guidance on safe use of the equipment. 
Care must be taken while lifting the weights on and off the machine. 
Put all the weights back in the proper place after use.

PROCEDURE 
 
For each beam,...

David · Accepted Answer

The theoretical horizontal and vertical deflections for beam 1 are: 
   
   
   
   (  ) 
   
    
  
(
 
 
 
 
 
)   (  ) 
The theoretical horizontal and vertical deflections for beam 2 are: 
   
    
  
   (  ) 
   
    
   
   (  ) 
The theoretical horizontal and vertical deflections for beam 3 are: 
   
   
   
   (  ) 
   
    
   
(
 
 
 
 
 
)   (  ) 
Where,
  
   
  

Load         
W           
(N) 
Beam 1 Beam 2 Beam 3 
Theoretical Theoretical Theoretical 
δv mm 
δH 
mm 
δv mm 
δH 
mm 
δv mm 
δH 
mm 
0 0 0 0 0 0 0 
10 0.12051 0.2025 1.272345 1.62 0.636173 0.405 
20 0.241021 0.405 2.54469 3.24 1.272345 0.81 
30 0.361531 0.6075 3.817035 4.86 1.908518 1.215 
40 0.482042 0.81 5.08938 6.48 2.54469 1.62 
50 0.602552 1.0125 6.361725 8.1 3.180863 2.025 
60 0.723063 1.215 7.63407 9.72 3.817035 2.43 
Table 1:

Department of Mechanical and Civil Engineering EN200: Applied Mechanics Lab. Bending of Thin Curved Beam OBJECTIVES To estimate the theoretical end displacements of three arrangements of bar and to...

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