HITEC UNIVERSITY Three Point Bending Test By Group#04 Members Name Usman Rasheed (ME-131) Sarnad Ali Shah (ME-108) Farrukh Muhummad Aoun (ME-30) Shahzaib bakht (ME-84) Hafiz Abdul Hadi ()ME-32 A PROJECT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE COURSE OF MECHANICS OF MATERIALS IN MECHACNICAL ENGINEERING B. Sc. Mechanical Engineering HITEC UNIVERSITY January, 2011 Projector Supervisor’s: Mr. Sheharyar Malik Taxila, Pakistan January, 2011 ABSTRACT In this report different mathematical models for a ballistic missile are derived and simulated for the complete guided control system.In this research work V-2 rocket is taken as an example.
Equations of motion are used in SIMULINK to perform simulations. An optimum trajectory is in accordance with launch angle and different burnout parameters. The missile would follow this ideal trajectory in the absence of any disturbance. But in real flight there are various errors and perturbations that make the vehicle not to follow the designated path.
To have a successful flight it is required to remove the effect of these disturbances through a properly designed control and guidance system. DOF program is simulated which is then incorporated with the pitch orientation controller and a roll stabilization controller and results are simulated in accordance. Inertial navigation mechanization model is constructed in Simulink to propose an ideal navigation model for the rocket system. The controller analysis is performed at various points in the trajectory and the measurements are made in frequency domain.
A comprehensive roll control model is designed along with pitch controller using Simulink and various frequency domain plot; bode plots & root locus for analysis.Aim To calculate the modulus of elasticity in bending Ef, flexural stress ? f, flexural strain ? f and the flexural stress-strain response of the material by performing three point bending flexural test Theory This test measures the flexural strength and flexural modulus of reinforced and unreinforced plastics. These calculations allow you to choose materials that do not bend when supporting the loads you require for your application. These calculations relate to the stiffness of your material.The test uses a universal testing machine and a three point bend fixture to bend plastic test bars to acquire the data needed to make the calculations. The calculations and set-up for D790 are more complex and time consuming compared to other tests so please read the entire specification from ASTM before running the test.
ISO-180 is similar in concept to this test although the specimen shapes and some other details are slightly different. This is a simple summary to help you determine if this specification is right for you and also to call out what testing equipment is needed.Load This is the amount of force that is applied to the specimen, as measured by the loadcell in the testing machine, and is expressed in either lbf, kgf or N (pounds of force, kilograms of forceor Newtons) Extension This is the amount of travel that is required to apply the load and is measured in inches or mm Stress This is the amount force applied divided by the cross-sectional area. Typically, the cross-sectional area of the specimen that isused is the original cross section of the gauge length area of thespecimen, and this is commonly referred to as the engineeringstress.In some labs and applications, true stress is used; this is the load divided by the actual cross-sectional area; as the test proceeds, test specimens typically thin out, or neck, as the test proceeds so true stress becomes very difficult to measure since the cross sectional area is changing. Stress is measured in psi or MPa (pounds per square inch or megapascals).
Strain Strain is measured as the change in length of the gage length divided by the original gage length. Since this is really a ratio, strain is measured in %.Hooke's Law Almost every material obeys Hooke's Law, which states that if a load is applied to a material, it will deform in a proportional manner to the amount of applied load. While its true that most materials obey Hooke's Law, they only obey this up to the limit of proportionality. Modulus of Elasticity The modulus of elasticity is simply the ratio of stress to corresponding strain below the proportional limit of the specimen. Put another way, it is the slope of the stress vs strain graph in the elastic region of the test.
This is also referred to as Youngs modulus; since it is calculated as the stress divided by the strain, it has units of psi or N/mm2 Yield Point This is the point at which it is considered that the proprtional limit and behaviour has stopped and the material has entered into the 'plastic' zone. It is recognised by convention, as the point where there is an increase in strain without a corresponding increase in stress. Ultimate Point This is the point at which the maximum stress the specimen and material is capable of withstanding is reached. Breaking Point.
This is the point at which the sample finally breaks. It should be noted that the Breaking point and the Ultimate point are, more often than not, two seperate, distinct points on the stress / straingraph. Readings Material name = Marble type brittle material (rectangular specimen) Length of specimen = L = 30cm Thickness of specimen = d = 12mm Width of specimen = b = 46mm Specimen no. | Load max (P) (KN)| Max Deflection (D) (mm)| Stress (? ) (mpa)| Strain (? )| Modulus of elasticity (E) (Gpa)| 1| 0.
2| 0. 30| 13. 646| 2. 4E-4| 58.
86| 2| 0. 18| 0. 18| 12. 282| 1.
44E-4| 85. 29| 3| 0. 24| 0. 24| 15. 31| 1.
99E-4| 76. 84| Ave. modulus of elasticity (E) = 73. 66 Gpa Conclusions In this experiment we observed the modulus of elasticity of brittle material is very low an in stress strain diagram of brittle material is the plastic portion is very less almost negligible and also the value of strain is very less. The material break at very small value of applying load so that type of material showing very less stain energy density and ability to absorbed strain energy is very small.
