5. A beam is 15 x 15 mm in cross-section, and it is 0.95 m long. It is pinned at both ends, and the value for Young's modulus is 135 GPa. What is the critical stress to cause buckling?
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The length of the beam,
The beam is pinned with both ends so the effective length of the beam,
Now, the minimum moment of inertia of the beam,
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- A wood beam is strengthened using two steel plates as shown in Fig, a. The beam has simple supports and an overhang and is subjected to a point load and a uniform load as shown in Fig. b. Calculate the maximum tensile and compressive stresses of the beam. Assume that Ew= 11 GPa and Es= 200 GPa.A steel pad supporting heavy machinery rests on four short, hollow, cast iron piers (see figure). The ultimate strength of the cast iron in compression is 400 MPa. The total load P that may be supported by the pad is 900 kN. Using a factor or safely 3.0 with respect to ultimate strength, determine the outer diameter of the pier if the thickness, is of the cross section is 12 mm.A column, pinned at top and bottom, is made up of two C 6 x 13 steel shapes (see figure) that act together. Find the buckling load (kips) if the gap is zero. Find required separation distance d(inches) so that the buckling load is the same in y and z directions. Assume that E = 30,000 ksi and L = 18 ft. Note that distance d is measured between the centroids of the two C shapes.
- Solve the preceding problem using the following data: beam cross section is 100 x 150 mm, length is 3 m, and point load is P = 5 kN at mid-span, Point C is located 25 mm below the top of the beam and 0.5 m to the right of support A.-15 A composite beam is constructed froma wood beam (3 in. x 6 in.) and a steel plate (3 in, wide). The wood and the steel are securely fastened to act as a single beam. The beam is subjected to a positive bending moment M. = 75 kip-in. Calculate the required thickness of the steel plate based on the following limit states: Allowable compressive stress in the wood = 2 ksi Allowable tensile stress in the wood = 2 ksi Allowable tensile stress in the steel plate = 16 ksi Assume that Ew= 1,500 ksi and es= 30,000 ksi.An aluminum bar having a rectangular cross section (2.0 in. × 1.0 in.) and length L = 30 in. is compressed by axial loads that have a resultant P = 2800 lb acting at the midpoint of the long side of the cross section (sec figure). Assuming that the modulus of elasticity E is equal to 10 × 106 psi and that the ends of the bar are pinned, calculate the maximum deflection and the maximum bending moment Mmax.
- A wood beam AB with a rectangular cross section (4 in. × 6 in.) serving as a roof purlin is simply supported by the top chords of two adjacent roof trusses. The beam is subjected to distributed load q acting in the vertical direction through the centroid of the purlin cross section. The top chords of the trusses have a slope of = 27°. The purlin has length L =75 in. Determine the permissible distributed load q based on the allowable compressive and tensile stress in the beam eall = 2 ksi.A flat steel bar, 26 mm wide by 5 mm thick and 1.6 m long, is bent by couples applied at the ends so that the midpoint deflection is 24 mm. Compute the maximum stress in the bar. Use E = 220 GPa. Answer must be in MPa.A circular Euler column with one end fixed and the other pinned (or hinged or simply-supported) is under a compressive axial load. Given the length L of the column and bending rigidity EI, what is the buckling load Pcr ?
- If a force of 300 kN is applied to the top of a circular steel bar with a diameter of 150mm and a length of 300mm, reducing the length of the reaxial direction by 0.16mm, and increasing the diameter of the cross section by 0.01mm, what is the modulus of elasticity E and poisson's ratio of the steel rod?a rectangular beam with a span of 20ft is simply supported at both ends. The maximum flexural stress for the beam is 1200 psi and the dimensions of its cross-section are: b=4 in and h=10 in. If the beam is to be loaded at mid-span with a concentrated load of 2000lbs, will the beam collapse?Q1 A steel beam of I cross-section is simply supported on a span of 4m. Find the safe uniformly distributed load the beam can carry if the tensile stress is not to exceed (60) N/mm2. Also find the maximum compressive stress.