A solid steel column and a hollow steel column, both have the same length and same cross-section area, and are fixed at the ends. If the internal diameter of hollow column is 2/3 of its external diameter, find the ratio of buckling strengths of solid steel column to that of hollow steel column.

The prismatic rod shown is made of a steel that is assumed to be elastoplastic with E = 200 GPa and oy = 280 MPa. Knowing that couples M and M' of moment 525 N·m are applied and main- tained about axes parallel to the y axis, determine (a) the thick- ness of the elastic core, (b) the radius of curvature of the bar. y M 18 mm 24 mm X 'M'

A compound bar consisting of bronze, aluminum, and steel segments is loaded axially as shown in the figure. Determine the maximum allowable value of P if the change in length of the bar is limited to 2 mm and the working stresses prescribed in the table are not to be exceeded. E=200 GPa A=D300mm? L=3m 2m 2 m 3m 1.5m Match each tem to a choice

Q3/ compare shape factor (, for stiffness-limited design in bending of a square box section of outer edge-length h 100mm and wall thickness t = 3mm. Is this shape more efficient than one made of the same material in the form of a tube of diameter 2r 100mm and wall thickness t= 3.82 mm (giving it the same mass per unit length, m/L)? Treat both as thin-walled shapes. Take the solid square section as standard. I= nr3t (for the tube), I- h*t(1 + 3) I= bh/12 (for square box section), (for standard solid square section) (for square box section), (for the tube) A=D4 th A=2n rt h

The aluminum W 310 x 202 (wide flange) column is subjected to an eccentric axial load P as shown. The maximum compressive stress in the column is given by the so-called secant formula: where --- [¹ + ( √5)] ec o 1+ sec max E ō = P/A = average stress A = 25800 mm² = cross-sectional area of the column e = 85 mm = eccentricity of the load c = 170 mm = half depth of the column r = 142 mm = radius of gyration of the cross section L = 7100 mm = length of the column E = 71 x 10⁹ Pa = modulus of elasticity Determine the maximum load P that the column can carry if the maximum stress is not to exceed 120 × 10^6 Pa. Terminate the computation when Σa < 0.0005%.

A cylindrical assembly consisting of a brass core and an aluminum collaris compressed by a load P (see figure). The length of the aluminum collarand brass core is 350 mm. the diameter of the core is 25 mm, and theoutside diameter of the collar is 40 mm. Also, the module of elasticity ofthe aluminum and brass are 72 GPa and 100 GPa, respectively.(a) If the length of the assembly decreases by 0.1% when the load Pisapplied, what is the magnitude of the load?(b) What is the maximum permissible load f^ if the allowable stresses inthe aluminum and brass are SO MPa and 120 M Pa, respectively?

Fundamental Deformable Bodies

A simply supported beam, circular in cross section, of span L supports a point load W at mid span. The length of elastic-plastic zone at the plastic hinge will be A 0.33 L B 0.41 L C 0.50 L D 0.58 L

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A steel beam is welded at the left and loaded as shown below. It has a rectangular cross section (height=h, thickness=t) with L=1m, a=0.4 m, h=3 cm, t=1 cm, F=500 N, w=200 N/m. a. Find the factor of safety if the material is 1020 Steel that has been hot rolled (hint: ductile) using an appropriate failure theory b. Find the factor of safety if the beam is the materials is gray cast iron number 50 (hint: brittle) using an appropriate failure theory. а F W