3. The Z section in Fig. (a) 1s formed from aluminum alloy 2024-T3 sheet. What compressive stress will start local buckling of an element of the member? kw=2.9 E=10,700,000psi -75 RT Flange Web 0.65 1.05
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- 333 of o, and a, if the principal stresses are known to be 20 MPa and -80 935. For the element shown in Fig. P-935, determine the values MPa. 30 MPa 2つ 88 30 MPa Figure P.-935. XQ1 A truss system is shown in Figure Q1. It is loaded at joints D and E as shown. The truss members are to be manufactured from Aluminium Alloy cylindrical bar with a tensile yield stress of 300 MPa, a compressive yield stress of 200 MPa, and Young's Modulus of 70 GPa. 1.5m 1.5m A B 4001 10 KN 3m Fig. Q1 E 水 20 KN 1.5m D ➜ (a) Show that the truss system can be described as statically determinate. (b) Draw a Free Body Diagram of the truss and determine the reactions at the supports. (c) Use the METHOD OF JOINTS to determine the load in each member of the truss, indicating whether they are tensile or compressive.Question 6 The state of plane stress shown in Fig. Q6 occurs at a critical point of a steel component. The tensile yield strength oy 200 MPa for the grade of steel used. Use Mohr's circle to determine the factor of safety k with respect to yield using = (a) the maximum-shearing-stress criterion, and (b) the maximum-distortion-energy criterion. 40 MPa 25 MPa Fig. Q6 80 MPa
- A thin polymer plate PQR is deformed so that corner Q is displaced downward by a distance L = 1.45 mm to new position Q' as shown. Determine the shear strain at Q' associated with the two edges (PQ and QR). 120 mm 480 mm. P R 240 mm -2692 μrad -3352 μrad O-4917 prad -3610 μrad O-2921 urad Q 'Q' XProb. 2.9-10. At room temperature (70°F) and with no axial load (P = 0) the extensional strain of the prismatic bar (Fig. P2.9-10) in the axial direction is zero, that is, € = 0. Subsequently, the bar is heated to 120°F and a tensile load P is applied. The material properties for the bar are: E = 10 × 10³ ksi and a = 13 x 10-6/F, and the cross-sectional area of the bar is 1.8 in². For the latter load-temperature condi- tion, the extensional strain is found to be €x = 900 × 10 6. (a) Determine the value of the axial tensile load P. (b) De- termine the normal stress and the shear stress on the oblique plane NN'. (Note: The total strain is the sum of strain asso- ciated with normal stress o (Eq. 2.14) and the strain due to change of temperature AT (Eq. 2.8).) in. P Gage measures extensional strain Ex N N' 25° P2.9-10 XPROBLEM 1) An aluminum bar carries the axial loads at the positions shown. If E=70GPA, compute the total deformation of the bar. Assume that the bar is suitably braced to prevent buckling. 0.4m D What is the axial stress o Ag in Pa? 10KN 0.8m 0.4m B 5KN 0.6m 20KN A=800 mm? A=1,200 mm²
- The assembly in Fig. P-242 consists of a light rigid bar AB, pinned at O, that is attached to the steel and aluminum rods. In the position shown, bar AB is horizontal and there is a gap, A = 5 mm, between the lower end of the steel rod and its pin support at C. Compute the stress in the aluminum rod when the lower end of the steel rod is attached to its support. A 0.75 m O Steel A = 250 mm² E = 200 GPa 1.5 m Figure P-242 Aluminum L = 2 m A = 300 mm² E = 70 GPa BDEFORMATION DUE TO AXIAL FORCES PROBLEM 1: CE Brd Exam The rigid block shown weighs 176.4 kN. It is held in position shown with stress in the supporting rods shown initially zero. If the former is to remain horizontal when released, 1a. Find the ratio of forces in bronze and steel a. 0.389 c. 0.397 1b. Find the stress in the bronze rod. b. 0.344 d. 0.416 а. 31.92 MPа с. 28.73 МPа 1c. Find the the elongation of steel rod. b. 53.34 MPa d. 39.67 MPa a. 0.615 mm b. 1.83 mm c. 2.31 mm d. 2.12 mm 0.6 m BRONZE A=900mm STEEL STEEL A=600mm A=600mm 1 m E-200GPA E-83GPA E=200GPA W = 176.4 kNAn aluminum bar carries the axial loads at the positions shown. If E=70GPA, compute the total deformation of the bar. Assume that the bar is suitably braced to prevent buckling. 0.4m D 1) What is the deformation 8Ag in mm? 10KN 0.8m 0.4m 5KN 0.6m 20KN A=800 mm? A=1,200 mm²
- Bar AB has a cross-sectional area of 1200 mm² and is made of a steel that is assumed to be elastoplastic with E = 200 GPa and σ y = 250 MPa. Knowing that the force F increases from 0 to 520 kN and then decreases to zero, determine (a) the permanent deflec- tion of point C, (b) the residual stress in the bar. A C a = 120 mm Fig. P2.122 -F 440 mm B4.3. At a point in a structural member, yielding occurred under a state of stress given by: 40 40 50 -60 MPa -60 Determine the uni-axial tensile yield strength of the material according to (a) maximum shearing stress theory, and (b) Octahedral shearing stress theory. 4.5. Determine the width t of the cantilever of height 2t and length 0.25 m subjected to a 450 N concentrated force at its free end. Apply the maximum energy of distortion theory. The tensile and compressive strengths of the material are both 280 MPa. 4.6. Determine the required diameter of a steel transmission shaft 10 m in length and of yield strength 350 MPa. In order to resist a torque of up to 500 N.m. The shaft is supported by frictionless bearings at its ends. Design the shaft according to the maximum shear stress theory, selecting a factor of safety of 1.5, (a) neglecting the shaft weight, and (b) including the effect of shaft weight. Use y = 77 kN/m as the weight per unit volume of steel. 190 MPa 30 MPa 40 MPa…Problem 4 For the shown structure, AB is made by A-36 steel (Est = 200GPA, ast = 12 x 10-67 °C) and BC is made by %| 73.1GPA, aal = 23 × 10-6/ °C). Both AB and BC are having circular cross sectional area. The aluminum (Eal gap between C and the rigid wall at D is initially 0.15 mm. For the following situations, find (1) reaction forces at fixed end A and D (2) Plot the axial load diagram P=400 kN applied at B and there is no temperature -0.15 тm 600 mm 600 mm vi. change vii. P=400 kN applied and temperature in both AB and BC 25°C segments had dropped AT P=400 kN applied, however, the temperature in AB increased ATst = 25°C and temperature in BC decreased ATal = 25°C vii. B. 25 mm 50 mm