Title : Shear Force and Bending Moment
Objective : To determine the shear force and bending moment when concentrated load, symmetrical load and non symmetrical load are applied
Introduction
The shear force (F) in a beam at any section, X, is the force transverse to the beam tending cause it to shear across the section. The shear force at any section is taken as positive if the righthand side tends to slide downwards relative to the left hand portion. The negative force tends to cause the right hand portion to slide upwards relative to the left. X
W
F
Shear force F = Load W but in opposite directions
W
The bending effect at any section X of a concentrated load W is measured by the applied moment Wx, where x is the perpendicular distance of the line of action of W from section X. This moment is called the bending moment M. x
X
M = Wx
The bending moment is balanced by an equal and opposite moment exerted by the material of the beam at X, called the moment of resistance. The bending moment is positive if its effect makes the beam to sag at the section considered. If the moment tends to make the beam bend upward or hog at the section, it is negative.
For any value of x, the relationship between load W and shearing force F is : W = dF / dx
And the relationship between shearing force and bending moment M is : F = dM / dx
Apparatus and Materials
1. Shear forces apparatus : 1 set of 80mm x 50mm x 38mm aluminium section with 2 adjustable span support. 2. 1 unit of shear force dynamometer.
3. 2 sets of weight hangers.
4. 1 set of weights.
5. 2m measuring tape.
Procedure
Shear force and bending moment experiment for concentrated load. 1. The 2 edge supports is set up on the base of the structural test frame at a distance of 800mm from edge to edge. 2. The shear force apparatus is placed on the supports. 3. The beam is horizontally aligned by adjusting the screws. 4. The weight hanger is placed in the centre of the beam (400mm from the support). 5. The screws is adjusted to repeat horizontal beam alignment. 6. The shear force and bending moment dynamometers is zeroed. 7. The weights is placed as given in table and the shear force and bending is noted. 8. When placing each weight the horizontal beam alignment was carried out and the dynamometers were zeroed. 9. The percentage error for each set of reading is calculated.
Shear force and bending moment experiment for symmetrical load 10. The 2 edge supports is set up on the base of the structural test frame at a distance of 800mm from the edge to edge. 11. The shear force apparatus is placed on the support. 12. The beam is horizontally aligned by adjusting the screws. 13. The weight hangers is placed at a distance of 100mm from the supports. 14. The screws is adjusted to repeat horizontal beam alignment. 15. The shear force and bending moment dynamometers is zeroed. 16. The weights is placed as given in the table and the shear force and bending moment values is noted. 17. When placing each weight the horizontal beam alignment was carried out and the dynamometers were zeroed. 18. The percentage error for each set of reading is calculated.
Results :
Case 1 Load at Midspan          
Span L, = 800.0 mm          
 0.800 m           
Lever arm = 0.180 m          
            

            
   M         
            
  V          
Reaction, R
            
 x 240 mm         
    ...