20, 40 20 Dimensions in mm PROBLEM 4.1 20 M= 15 kNm A Knowing that the couple shown acts in the vertical 80 plane, determine the stress at (a) point A, and (b) point B. [Ans. (a) -61.2 MPa (b) 91.8 MPa] 20 Fig. P4.1
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- Consider a long cylindrical solid rod - total length L - mass density p; - radius R1 = R2 = R; suspended from the top and hung freely downward along the (-1)Ž direction; - subjected to gravitational pull from the ground in the (-1)Ź direction. R2 +Z Z = h R1 Z = 0 a) Calculate the longitudinal stress o within the rod as a function of h; b) Repeat the calculation ifR| turns into a cone); = 0 and R2 = R (i.e., when the cylindrical rod c) Based on your answers to a) and b), provide some reasoning as to why a space elevator would not work [hint: think about the rod as the load bearing element of the space elevator].1. A circular shaft with a keyway can be approximated by the section shown in Fig. r=b Ay r r=2acose Figure 1: Circular shaft with a keyway. The keyway is represented by the boundary equation r = b and the shaft is represented by the boundary equation r = 2a cos 0. Show that using a Prandtl stress function of the form ²) (₁ (1-2a cos) X v = K (b² − ²) (1 – : will solve the problem of torsion on this shaft and find the constant K (assume an applied torque T). Compute the shear stress components Txz and Tyz. (Hint: start by converting the stress function to Cartesian coordinates).F2 Q1) Axial displacement of point C in the system shown on the left is 0.01 cm. Find the maximum elongation of the bar and the maximum normal stress. A F1 A. GIVEN: F2 = 100 kN, (1 = 240 cm, €2= 160 cm, bi = 5 cm, bz=10 cm, h=5 cm, E=2.107 N/em², a=20 cm Note: neglect stress concentration. h bị b2 A-A section
- Q1: A circular steel rod ABCD is loaded as shown below. Use the following data to Find the maximum stress and the deformation (AL) of the rod. Take E = 200 GPa. A P1 L1 Dia. 1 L2 Dia. 2 C L3 P2 D D 30 mm o P3 Dia. 1 Dia. 2 P1 P2 P3 L1 L2 L3 Name (mm) (mm) (kN) (kN) (kN) (mm) (mm) (mm) 45 40 100 35 30 1300 2100 1300b2 h G B M. Q4) For the given system; a) Draw internal force diagrams and determine the most critical section. b) Show the stress distribution on this critical section and find the maximum normal stress. GIVEN: (1 = 50 cm, {2= 30 cm, M, = 5000 Nem, q. = 20 N/cm, bị = 4 cm, b2 = 2 cm, h = 4 cm, t= 1 cmProblem 2: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 18 ksi, oy = 24 ksi, and Txy = 15 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 24 ksi бу 18 ksi 15 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the stress components Ox, Oy, and Txy on an element rotated 25° counter-clockwise from the original element shown. Label all of these quantities on the circle. (c) Show all stresses from part (b) on a properly oriented stress element. Be sure to include all stress components acting on the element.
- Course A force of 700 N is applied on a rigid bar as shown in the figure. The moment of Fabout origin O in clockwise direction is. 4 m 60° Select one: O a. 2424.8N.m Ob. 732 N.m Oc2732 N.m Od. 1000 NmH.W no. 2 Q1) 28 N.m torque is needed to turn the bolt around its axis as shown in the Figure (1) below. Find the force F and the forces between the wrench's smooth face jaws and the hexagonal bolt head's corners A and B. Suppose the wrench fits on the bolt simply such that connection is only formed at corners A and B. 150 mm 14 mmQuestion 2) arm of Figure B from point x z plane, a horizontal angle of θ = 44 ° angled F = 26 kN size and a force C at the point z in the direction of M = 18 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.6 m and L 2 = 1.3 m . It is desired to determine the stress state of point A on the aa section taken from the arm. The radius r of the section is r=0.029 m and the shear modulus of the sleeve material is also G = 79 Gpa . According to this; Question 2-C) Find the normal stress caused by the normal force at point A ( Write your result in MPa .) Question 2-D) Find the normal stress caused by the bending moment at point A. (Your result MPa in the size of your font.)
- Question 2) arm of Figure B from point x z plane, a horizontal angle of θ = 44 ° angled F = 26 kN size and a force C at the point z in the direction of M = 18 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.6 m and L 2 = 1.3 m . It is desired to determine the stress state of point A on the aa section taken from the arm. The radius r of the section is r=0.029 m and the shear modulus of the sleeve material is also G = 79 Gpa . According to this; Question 2-A) Find the shear stress at point A due to the shear force . ( Write your result in MPa .) Question 2-B) Find the shear stress due to the torsional moment at point A. ( Write your result in MPa .) Question 2-C) Find the normal stress caused by the normal force at point A ( Write your result in MPa .) Question 2-D) Find the normal stress caused by the bending moment at point A. (Your result MPa in the size of your font.)3.12 The stress matrix referred to axes Px,x,x3 is given in ksi by 14 21 [o,]- 0 21 21 Let rotated axes Px,x,x, be defined with respect to axes Px,x,x3 by the table of base vectors ê, ê, 2/7 3/7 6/7 3/7 -6/7 2/7 6/7 2/7 -3/7 (a) Determine the stress vectors on planes at P perpendicular to the primed axes; determine tei), te2), and tes) in terms of base vectors ê,, ê, , and ê, .Question 2) arm of Figure B from point x z plane, a horizontal angle of θ = 44 ° angled F = 26 kN size and a force C at the point z in the direction of M = 18 kn.m acts a moment in size. The lengths of the arm are also given as L 1 = 1.6 m and L 2 = 1.3 m . It is desired to determine the stress state of point A on the aa section taken from the arm. The radius r of the section is r=0.029 m and the shear modulus of the sleeve material is also G = 79 Gpa . According to this; Question 2-A) Find the shear stress at point A due to the shear force . ( Write your result in MPa .) Question 2-B) Find the shear stress due to the torsional moment at point A. ( Write your result in MPa .) Question 2-C) Find the normal stress caused by the normal force at point A ( Write your result in MPa .)