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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![20
40
20
Dimensions in mm
PROBLEM 4.1
20
M = 15 kNm
Knowing that the couple
80
shown acts in the vertical
plane, determine the stress at
(a) point A, and (b) point B.
[Ans. (a) -61.2 MPa (b) 91.8
MPa]
20
В
Fig. P4.1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c9c3259-16b0-44c2-9416-39962bcc9c3e%2F5f079107-d4e1-435d-96c4-05288781c963%2Fk960ow_processed.jpeg&w=3840&q=75)
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- 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 sectionConsider 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).
- b2 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.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 1300
- 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 Nm3.12 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-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.)H.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-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 .)