5. In the case of bending the member until the yield strain is reached in some, but not all, of its compression elements before lateral buckling occurs, it is referred to as a. local buckling b. elastic buckling c. inelastic buckling d. bending failure e. shear failure

Two portions of member AB are glued together along a plane forming an angle θ with the horizontal. Knowing that the ultimate stress for the glued joint is 2.5 ksi in tension and 1.3 ksi in shear, determine the range of values of θ for which the factor of safety of the members is at least 3.0.

Q.2.

Problem 2 The rigid bar is plnned at A and held by two flexible bars at E and C. The load P Is applled at B. The two flexible bars FE and DC each have a diameter of 1 In. The flexible bars are elastic- perfectly plastic with a yleld stress equal to 20 ksl and a yleld strain of 0.001. Determine the following: The load R, at first yleld and the corresponding deflection at B, &, The ultimate load Pu and the corresponding deflection du The permanent deflection and residual stresses in each rod if the ultimate load is removed Construct P - A curve showing yield, ultimate and permanent deformation o (ksi) 1 ft E F 1 ft1 ft 20 B P e (in./in.) 0.001 1 ft D 2 ft 1 ft A

(c). At a point in an elastic material the stresses on three mutually perpendicular planes are as follows: First Plane: 50 MPa tensile and 40 MPa shear Second plane: 30 MPa compressive and 40 MPa shear Third plane: No stress Find, (i) The position of principal planes and the magnitude of principal stresses.

A plane element is subjected to the stresses as shown in Fig. Determine (a) the principal stresses and their directions and (b) the maximum shearing stresses and the directions of the planes on which they occur. 70 MPa 35 MPa 40 MPa

Problem 2. [Concepts: Internal forces in 2D and average normal stress] The bars of the truss each have a cross-sectional area of 1.25 in². a) Determine the average normal stress in each member due to the loading P = 8 kip. State whether the stress is tensile or compressive. b) If the maximum average normal stress in any bar is not to exceed 20 ksi, determine the maximum magnitude P of the loads that can be applied to the truss. 4 ft 4 ft 4 E 0.75 P 0

Prob. 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 X

The ends of the compound shaft are attached to rigid walls. The maximum shear stress is limited to 60 MPa for the bronze segment AB and 84 MPa psi for the steel segment BC. Determine the diameter of each segment so that each material is simultaneously stressed to its permissible limit when the torque T = 40 kN-m is applied as shown. The shear moduli are 35 GPa for bronze and 80 GPa for steel. Bronze Steel B A T 3 m 2 m

For the truss shown in figure, (a) determine the stress developed in member FH if it has a cross-sectional area of 1200 ??? (b) determine the stress developed in member AB if it has a cross-sectional area of 1100 ???.