If the ext ended st ress is given by matrix 2x 0 12 0 3y 8 12 8 The volumetric force Fy= %3D aDl wrong =-3 =2 =3
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- 5/5 find the normal stress at left of point C A 100 C 40 kN 50 kN 40 mm 70 10 kN 20 mm 30 mm 100 mm 300 mm 300 mm 200mm B.If the extended stress at the point p in the level and at i+j+ k is given by matrix 10 2 2 22 the component Tnx = 231 1 %3D nx V3 nx V3 aņl wrong %3DF2 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
- 3 1 4 tIf the components of stress at pointp given by 1 2-5 Mpa, 4 -5 0 then the stress vector whose unit normal parallel to plane 2x +y-z=1 is (V(3/2), 3V(3/2), 3/(3/2)) .10 (V(3/2) 3V (3/2), V(3/2)) I1O ((3/2) , 2V(3/2), 2 v(3/2)).1 Oa) Determine the internal axial force in the aluminum section, specify tension or compression b) Determine the internal axial force in the copper section, specify tension or compression c) Determine the internal axial force in the steel section, specify tension or compression d) Determine the axial displacement between point A and point D e) If the aluminum section has a v = 0.3, determine the change in diameter of the aluminum rod Aluminum Copper Steel Eal = 10(10³) ksi Ecu = 18(10³) ksi E = 29(10³) ksi AAB = 0.09 in² ABC = 0.12 in² AcD = 0.06 in² %3D 3.50 kip 1.75 kip 2.00 kip 1.50 kip A D B 3.50 kip 1.75 kip -18 in.- -12 in.→ -16 in.-Determine the state of stress at point q. The pipe has an inner diameter of D₁ = 1.0 in and an outer diameter of = 1.8 in. Use the exact expression for Q, if needed. Label the reultant forces on the cross section below. Report your answer (3x3 matrix) in psi to one decimal place. Do 4 in. Y 4 in. 150 lb 6 in. 50 lb 10 in. 200 lb 150 lb X N Y
- A stress element in a rock mass making up a slope experiences a 2D stress as follows: σx = 8 MPa, σy = 4 MPa , tauxy = 3 MPa A. By using the stress transformation equation, draw a curve of the stress variation experienced by the stress element at the axis of rotation angle θ = 0-180°. Use the interval θ = 1°, with the x-axis and stress as the y-axis. Mark on the curve where the principal stress and maximum shear stress occur. Draw the three stress curves completely and neatly B. Draw the stress element along with the magnitude and direction of the stress at the angle where the principal stress occurs and at the angle where the maximum shear stress occurs. C. Write down the direction vectors of the orientation of the principal stress (n1, and n₂) and the maximum shear stress (nmax). Write it in unit vector form i and j. D. Prove that the value of the stress invariant (I1, and I2) using the principal stress is reached and prove that the orthogonality condition of the direction cosine is…1-26. What is the required diameter of the pin Bfor the bell crank mechanism shown in the figure if an applied force of 60 kN at A is resisted by a force P at C? The allowable shearing stress is 100 MPa. Ans, 23.2 mm. 60 N A 150 mm 300 mm Pin BThe state of stress at a point in a machine component is given by ox = 120 MPa, oy = 55 MPa, Oz = -85 MPa, Oxy = -55 MPa, Oxz = -75 MPa, and oyz = 33 MPa. Construct the Mohr's circles of stress for this stress state and find the maximum shear stress.
- The shear stress is maximum on the principal plane Select one: O True O FalseBelow Figure shows the section of an angle purlin. A bending moment of 60 5 kN.m is applied to the purlin in a plane at an angle of 30 deg to the vertical y axis. If the sense of the bending moment is such that both its components Mx and My produce tension in the positive xy quadrant, calculate the maximum direct stress in the purlin, stating clearly the point at which it acts. * 100 mm BỊ 10mm 30° C ID 10mm 57 MPa. 89 MPa. Non Above 72 MPa. 125mmDirect a key d the Hub Shear plane Hub Key F2 y, or anical F1 T=Torque Shaft T=F(D/2) F = Force of shaft on key F= Force of hub on key Side view -D Shaft diameter End view Shear Shaft plane Hub F1 Key F2 Shear area = A, = bxL %3D Enlarged view of key Pictorial sketch of key, shaft, and hub Ноу