5. A 4-point bending test is performed on a beam of length L = 1 m. A load of P = 2000 N is applied across two loading points a distance a = 0.4 m from the sides of the beam. If the beam has a radius of r = 1 cm and a yield strength of σ = 250 MPa, does the bar yield? If it's an elastic-perfectly plastic material, does it fail all the way through the thickness of the bar? What would the yield strength of the material need to be if we wanted a factor of safety of 1.5?

After load P is applied to the pin-connected structure, a normal strain of = +650 µe is measured in the longitudinal direction of member (1). The cross-sectional area of member (1) is A₁ = 0.6 in.2, its elastic modulus is E₁ = 31000 ksi, and its yield strength is 33 ksi. Assume a=6.25 ft, b=7.75 ft, c=4.5 ft, and d=3.75 ft. (a) Determine the axial force in member (1), the applied load P, and the resultant force at pin B. (b) The ultimate shear strength of the steel pins is 52 ksi. Determine the minimum diameter for the pin at B if a factor of safety of 2.2 with respect to the ultimate shear strength is required. (c) Compute the factor of safety for member (1) with respect to its yield strength. (1) a D Answer: 0₁ = 1.6377 B (a) Determine the axial stress o, in member (1). ksi. b

A rectangular bar of length L has a slot in the central half of its length. The bar has width b, thickness t, and elastic modulus E. The slot has width b/3. The overall length of the bar is L = 520 mm, and the elastic modulus of the material is 74 GPa. If the average normal stress in the central portion of the bar is 190 MPa, calculate the overall elongation of the bar. Answer: 6 = b IN -1/2- b 6/3 mm

An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 620 mm. The cross-sectional dimensions of the beam are b₁ = 39 mm, d₁ = 94 mm, b₂ = 23 mm, d₂ = 23 mm, and a = 8 mm. For this material, the allowable tensile bending stress is 17 MPa, and the allowable compressive bending stress is 11 MPa. Determine the largest moment M that can be applied as shown to the beam. ak a ↓ a M B A Answer: M = i L N•m b₁