Objectives:
- Understanding the free-body diagrams FBD for bending and drawing the moment and shear diagrams for simply supported beam.
- Calculation of bending stress and deflection caused by the load, and the moment of inertia of different cross-sections.
- Obtaining the Modulus of Elasticity from deflection formula.
- Understanding the concept of Neutral Axis N.A and Neutral Plane and the difference between layers in compression and tension in bending.
- Performing practical bending test on a specimen according to specific standards to test the ductility of it.
Introduction:
Ductility is the ability of a material to withstand permanent deformation without breaking.
The bend test is a method for evaluating ductility by applying a load (P) at the midpoint of a simply supported beam with length (L).
Using the equations of equilibrium we can find that the forces on the beam at supports are normal and equal to P/2 on each. (There are no more external forces acting).
In order to determine the internal forces we use the method of sections from which we can draw the shear and moment diagrams as follows:
The stress at any point on the surface of the specimen can be determined by this formula: σ=(M y)/I
While acting with a force (P), the higher surface of the specimen is confronted with compression force while the lower surface is confronted with tension force.
The Neutral Axis N.A and Neutral Plane are somewhere between the two layers (compression and tension) where there is neither tension nor compression.
Calculating the stress at the higher surface we find that it is negative (compression) while the stress at the lower one is positive (tension).
Theoretically the stress at the Neutral Plane must be zero.
When we apply the load (P) some deflection (δ) will occur in the beam, this can be determined by the following formula:
δ=(P L^3)/(48 E I)
Where E: is the Modulus of elasticity.
P: is the applying load.
L: the Length.
I: the moment of inertia of the cross section.
We can get the value of E (Modulus of Elasticity) of the specimen using this formula: δ=(P L^3)/(48 E I)
In this experiment we are interested in deflecting the specimen from its mid-point by 180o and seeing if it will fracture or not (whatever the necessary load is). Then we can determine if the specimen is ductile enough or not.
At the end of the bend test we can calculate the length of the specimen using this formula:
L=D+2d+2R+t
(t: clearance = (5-10) mm)
Method:
– The test is held on a Deformed Carbon-Steel Concrete reinforcement of 10 mm outside diameter according to standards.
– The specimen will be cut so it is adapted to the machine.
– Choose a mandrel of dimensions; D= 4 x d = 4 x 10 = 40 mm.
– Install the mandrel in the plunger.
– Calculate the length between supports which equals to: L = 50 + 40 + 20 + 10 = 120 mm.
– Adjust the supports to this distance.
– Put the specimen on the supports, then turn the machine on and let the mandrel move to bend the specimen at a U shape with the specified angel 180o.
– If the specimen holds up it then it complies with the standard requirements and it is accepted.
– Otherwise any crack occurs the specimen doesn’t follow the requirements and it is rejected.
* The full report can be found in the attached PDF file below, 17-20
Bending Test.pdf