Consider a bar that is fixed at the left end and subjected to two forces as shown in the Fig. 3. Assume that the Young's modulus E and the cross sectional area A are constants. Determine the internal axial force, strain, and displacement fields. Draw the axial force diagram.
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- - 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.A slightly tapered bar AB of rectangular cross section and length L is acted upon by a force P (see figure). The width of the bar varies uniformly From b2at end A to b1at end B. The thickness t is constant. (a) Determine the strain energy U of the bar. (b) Determine the elongation ?? of the bar by equating the strain energy to the work done by the force P.
- A bungee cord that behaves linearly elastically has an unstressed length L0= 760 mm and a stiffness k = 140 N/m. The cord is attached to two pegs, distance/? = 380 mm apart, and is pulled at its midpoint by a Force P = 80 N (see figure). (a) How much strain energy U is stored in the cord? (b) What is the displacement Scof the point where the load is applied? (c) Compare the strain energy (with the quantity PSC12. Note: The elongation of the cord is not small compared lo its original length.A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).A prismatic bar in tension has a length L = 2.0 m and cross-sectional area A =249 mn2. The material of the bar has the stress-strain curve shown in the figure. Determi ne t he elongation 5 of the bar for each of the following axial loads: P = 10 kN, 20 kN, 30 kN, 40 kN. and 45 kN. From these results, plot a diagram of load P versus elongation 5 (load-displacement diagram).
- A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?R= 76 A copper wire of length (400+R) cm , diameter of (4+R) mm and mass of (5000 + R) g, if Young's Module of copper is (100 + R) × 10°N/m² : a. Find the stress in the wire. b. Determine the strain. C. How much it will be lengthened if the original length is 3.7 m?The beam is supported by two wires AB and CD that have a diameter of 12 mm and 8 mm, respectively as shown in Figure Q2. Given the mass of the beam is 500 kg. i. Determine the position d of the 6 kN load so that the average normal stress in each wire is the same ii. Find the strain in wire CD, ɛcD iii. Using d that obtained in Question 2(i), calculate the displacement of point E B Wire AB Steel 6 kN D Wire CD L= 5 m Aluminium E= 200 GPa L=3 m E = 70 GPa E 10 m
- A set of strain rosette with three strain gauges at 120° apart is attached onto a steelstructure surface, point P for strain measurement. The state of stress at point P is thendetermined from the acquired strain measurement. The orientation of strain rosette isshown in Figure Q2. When the structure is being loaded the readings of the gaugesare 200μ, -100μ and -200μ at the directions of a, b and c respectively. a) Find the strains values in the x-y directions and draw the strain elementdiagram of that direction.b) Find the principal strain values and draw the strain element diagram of thatdirection.c) Find the maximum shear strain value and draw the strain element diagram ofthat direction.d) If the properties of the structure has E = 208 GPa and ν = 0.28, find themagnitude of the Principal Stresses and draw its stress element diagram.e) Give your comment without calculation on what happen to maximumprincipal strain of the steel (E = 208 GPa) is changed to titanium (E = 110GPa)?3) Objects 1 and 2 are positioned as shown in the figure. Object 1 is a rigid support. For object 2, following data is given: Object 1 Dimensions:20cm x 20cm x 150cm 4cm E = 70 GPa a = 11.7 E–6/°C If a 4 cm gap exists between two objects at room temperature, calculate the normal stress and strain in block Object 2 when the temperature is increased by 900°C 150cmA force P is applied to ring A connecting the two wires together. As a result, point A is displaced horizontally d = 2.1 mm. If L = 252 mm and 0 = 38°, what is the normal strain developed in wire AC? L