The rigid bar AB shown in figure is supported by a steel rod AC having a diameter of 20 mm and an aluminum block having a cross sectional area of 1800 mm². The 18- mm-diameter pins at A and C are subjected to single shear. If the failure (ultimate) stress for the steel and aluminum is (t) = 680 MPa & (a) i = 70 MPa respectively, and the failure (ultimate) shear stress for each pin is 900 MPa. Determine the largest load P that can be applied to the rigid bar AB if the factor of safety for the assembly is FS-2. Steel -0.75 m Aluminum 2 m- B A solid circular shaft ABC having a polar moment of inertia of J-15708 mm and shear modulus G = 80 GPa is subjected to two torques as shown. If T₁ =100 N.m, what should be the value of T2 for which the angle of twist at A will be zero. T₂ = ? N.m 800mm 800mm T₁ = 100 N.m A 60-N-m couple is applied to the rectangular steel bar given. Assuming that the couple is applied about the z axis as shown and knowing that E-200 GPa, what will be the radius of curvature of the bar? 12 mm 20 mm 60 N-m An overhanging beam was loaded by two concentrated loads and a clockwise moment through the arrangement shown in the figure. Knowing that the beam was made of steel with an allowable bending stress of (Gall 250 MPa) and an allowable shear stress of (Tall -90 MPa). a) Draw the shear-force and bending-moment diagrams for the lower beam ABC with the corresponding values on it. b) Determine the width of the beam if it is to be rectangular and have a height-to-width ratio of 1.25. 350 KN 200 KN.m Two wooden box beams (A and B) have the same outside dimensions (200 mm x 360 mm) and the same thickness (t =20 mm) throughout, as shown in the figure below. Both beams are formed by nailing and each nail has an allowable shear load of 230 N. Each beam is designed for a vertical shear force V-2.3 KN. (a) What is the maximum longitudinal spacing SA for the nails in beam A? (b) What is the maximum longitudinal spacing SB for the nails in beam B? (c) Which beam is more efficient in resisting the shear force? [= 20 mm 200 mm 360 mm 20 mm 200 mm 360 mm A horizontal beam AB is pin supported at end A and carries a load Q at C and end B, as shown in the figure. The beam is supported at C by a column which is fixed at the bottom D and pinned at the top C. The column is a made of solid steel bar (E-200 GPa, Gyield 250 MPa) having a square cross section. a) Based upon the critical load of the column, determine the allowable load Q if the factor of safety with respect to buckling is 1.5. b) Is Euler's equation valid for the calculation of critical buckling load. (Hint: Will the column fail in yielding or buckling first?) 2d- 1.6 m 50mm D -15m 15m+2.11 The horizontal rigid beam ABCD is supported by the vertical bars BE and CF and is loaded by the vertical forces P₁=400 kN and P2=360 kN acting at points A and D, respectively. Bar BE is also loaded by a vertical force P-200 kN acting at point G as shown. Bars BE and CF are made of steel (E=200 GPa) and have cross-sectional areas ABE-12600 mm² and ACF-9280 mm², respectively. Determine the vertical displacement at point B (i.e. 8B). P₁=400 kN P=200 kN 0.6m D P₂=360 kN