Question 2 The simply supported beam shown in Figure supports the triangular distributed loading. Determine its maximum deflection. El is constant. 2w Elastic curve

The deflection curve for a simple beam AB (sec figure) is given by v=q0L44EIsinxL Describe the load acting on the beam. Deter mine the reactions RAand RBat the supports, Determine the maximum bending moment Mmax.

Obtain a formula for the ratio c/maxof the deflection at the midpoint to the maximum deflection for a simple beam supporting a concentrated load P (see figure). From the formula, plot a graph of c/max versus the ratio a/L that defines the position of the load (0.5 < a/L < ) What conclusion do you draw from the graph? (Use the formulas of Example 9-3.)

A fixed-end b earn is subjected to a point load at mid-span. The beam has a rectangular cross section (assume that the h/b ratio is 2) and is made of wood (E = 11GPa). Find height h of the cross section if the maximum displacement of the beam is 2 mm. Calculate the displacement of the beam at the inflection points.

A symmetric beam A BCD with overhangs at both ends supports a uniform load of intensity q (see figure). Determine the deflection SDat the end of the overhang. (Obtain the solution by using the modified form of Castiglianos theorem.)

Copper beam AB has circular cross section with a radius of 0.25 in. and length L = 3 ft. The beam is subjected to a uniformly distributed load w = 3.5 lb/ft. Calculate the required load P at joint B so that the total deflection at joint B is zero. Assume that£ = 16,000 ksi.

A simple beam ABC DE supports a uniform load of intensity iy (see figure). The moment of inertia in the central part of the beam (BCD) is twice the moment of inertia in the end parts (AB and DE). Find the deflection Scat the midpoint C of the beam. (Obtain the solution by using the modified form of Castigliano's theorem.)

-10 The simple beam AB shown in the figure supports two equal concentrated loads P: one acting downward and the other upward. Determine the angle of rotation A at the left-hand end, the deflection 1under the downward load, and the deflection 2 at the midpoint of the beam.

Student ID is greater then 50

For the the given beam calculate the deflection of the beam at the center point and the reaction forces. (E-200 GPa, I = 16.67*10 mm) 2 m 2 kN/m 2m 5 kN/m