Strain and Stress Analysis: Pendulum Impact Test and Steel Plate Elongation
Explore the detailed analysis of strain and stress in materials through a pendulum impact test and determination of elongation in a steel plate under axial force. Understand lateral strain and Poisson's ratio effects under different stress conditions.
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Presentation Transcript
Impact Test Concluded The difference in height from which a pendulum is released and the height to which it rises after measure of the energy absorbed by the specimen and this is recorded on a dial mounted on a tester. impact gives a
A flat plate of steel, 1 cm thick, and of trapezoidal form tapers from 5 cm width to 10 cm width in a length of 40 cm. Determine the elongation under an axial force of 50 kN. E = 2 x 107N/cm2. Steel Diagram of a Trapezoidal l Plate t dx B1 P P B2 x L
Solution Consider a length, dx at a distance, x from width, B1, Width at that section L B B = + = + 2 1 B x B Kx 1 1 L B B = 2 1 where K Area (Ax) of chosen c/section = ( B1 + K x ) t. If the length dx elongates an amount du under load, its strain is: .1 du dx P A E =
Solution Contd. Total extension of bar, u z z z P P Kx t E ) L L = = u dx dx + A E x ( B 0 0 1 P dx + P L 0 L = = + u ln B Kx 1 t E B kx + KtE 0 1 B K L P = 1 u ln K t E B 1
Solution Contd. Substituting back for K, + B B B B P B = 1 2 1 u ln B 2 1 ( ) t E 1 L B B P B = 2 u ln B 2 1 ( ) t E 1 L In problem, t = 1 cm, B1 = 5 cm, B2 = 10 cm, L = 40 cm, P = 50,000 N, E = 2 x 107 N/cm2 50 000 , N 10 5 = = u ln 001386 . cm 10 5 40 7 ( ) x cm x 1 2 10 x
Solution Concluded Substituting back for K, + B B B B P B = 1 2 1 u ln B 2 1 ( ) t E 1 L B B P B = 2 u ln B 2 1 ( ) t E 1 L In problem, t = 1 cm, B1 = 5 cm, B2 = 10 cm, L = 40 cm, P = 50,000 N, E = 2 x 107 N/cm2 50 000 , N 10 5 = = u ln 001386 . cm 10 5 40 7 ( ) x cm x 1 2 10 x
1.9 Lateral Strain and Poissons Ratio Under the action of a longitudinal stress, a body will extend in the direction of the stress and contract in the transverse or lateral direction (see Fig. below). The reverse occurs under a compressive load.
Stress Effects P P Longitudinal Tensile Stress Effect P P Longitudinal Compressive Stress Effect
