Determine the free vibration frequency of the weightless frame shown in Fig. figure 1.17. Consider that the stiffness is the same and equal to El A X L/2 m C L/2 * Fig. 1.17 B Hom X h

Advanced structural engineering

A rigid bar of negligible weight is supported as shown in Fig. P-271. If W = 90 kN, compute the temperature change that will cause the stress in the steel rod to be 65 MPa. Assume the coefficients of linear expansion are 11.7 um/(m-°C) for steel and 18.9 µm/(m-°C) for bronze. Figure P-271 and P-272 Bronze L=3m A- 1300 mm E= 83 Gra Steel L- 1.5 m A= 320 mm E = 200 GPa -1m- 2.5 m 1.5m w

1. As seen in Fig. 1, a beam has two 1400 N. m loads applied to both of its ends. The beam is made of steel and, as can be seen, has a rectangular cross section. Find the maximum bending stress in the beam and show how it changes as the depth of the beam increases. 1400 N-m 1400 Nm FO 4 cm N.A.

(b-8b)+ (d-8d) Fig. 1.5 L + ÖL 1.9.1. For One-Dimensional Stress System. The relationship between stress and strain for a unidirectional stress (i.e., for normal stress in one direction only) is given by Hooke's law, which states that when a material is loaded within its elastic limit, the normal stress developed is proportional to the strain produced. This means that the ratio of the normal Lateral strain Poisson's ratio, u = Longitudinal strain Lateral strain = u x Longitudinal strain Problem 1.5. The safe stress, for a hollow steel column which carries an axial load of 2.1 x 10³ kN is 125 MN/m². If the external diameter of the column is 30 cm, determine the internal diameter.

The square element of a material undergoes the shear strain y. Assuming that y << 1, , determine the normal strains of the diagonals AC and BD.

Figure P24.25a shows a uniform beam subject to a linearly increasing distributed load. The equation for the re- sulting elastic curve is (see Fig. P24.25b) EI dx Note that the analytical solution for the resulting elastic curve is (see Fig. P24.25b) Wo(-x +24x -L*x) 120 EIL Use bvp4c to solve for the differential equation for the elastic curve for L 600 cm, E 50.000 kN/cm2, I 30,000 cm, and w 2.5 kN/cm. Then, plot both the numerical (points) and the analytical (lines) solutions on the same graph.

Without using tables find reactions using compatibility equation method

278. A rigid horizontal bar of negligible mass is connected to two rods as shown in Fig. P-278. If the system is initially stress-free, determine the temperature change that will cause a tensile stress of 60 MPa in the steel rod. -2 m 2 m 3 m 3 m Bronze A-1200 mm² E 88 GPa x = 18.9 pm/(m. °C) Figure P-278. Steel A = 900 mm? E = 200 GFa Q- - 11.7 m/(m. °C)

Determine the equivalent state of stress on an element at the same point oriented 30° clockwise with respect to the element shown in Fig Q11. Sketch the results on the element. | 75 MPa 100 MPa Fig Q10