A simply-supported beam of length $$3L$$ is subjected to the loading shown in the figure.

It is given that $$P = 1$$ $$N,$$ $$L = 1$$ $$m$$ and Young’s modulus $$E = 200$$ $$GP$$a. The cross-section is a square with dimension $$100$$ $$mm$$. The bending stress (in Pa) at the point A located at the top surface of the beam at a distance of $$1.5L$$ from the left end is _____________ .

(Indicate compressive stress by a negative sign and tensile stress by a positive sign).

The spring constant of a helical compression spring DOES NOT depend on

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that 𝑟₃ > 𝑟₁ and 𝑟₄ > 𝑟₂ , and that the areas of the cross-sections are the same. J₁ and J₂ are the torsional rigidities of the bars on the left and right, respectively. The ratioJ₂/J₁ is

A cantilever beam having square cross-section of side $$a$$ is subjected to an end load. If a is increases by $$19$$%, the tip deflection decreases approximately by