Mechanical Engineering Answers

For the rectangular element considered in Problem 10.52 and Fig. 10.35, find the element nodal force vector when a

concentrated (point) load, with Px0 ¼ 100 N and Py0 ¼ 500 N, act at the point (x0 ¼ 4 cm, y0 ¼ 5 cm). Perform the

needed integration by evaluating the integrand at the centroid of the element and treating the integrand as a constant

throughout the element.

For the rectangular element considered in Problem 10.52 and Fig. 10.35, find the element nodal force vector due to

distributed body force given by fx0 ¼ 0 and fy0 ¼ erg where r is the density of the material and g is the acceleration

due to gravity. Assume the value of r as 2800 kg/m3 and g ¼ 981 m/s2

. Perform the needed integration by evaluating

the integrand at the centroid of the element and treating the integrand as a constant throughout the element

For the rectangular element considered in Problem 10.52 and Fig. 10.35, find the element nodal force vector due to

uniform surface tractions, with Fx0 ¼ 1000 Pa and Fy0 ¼ 500 Pa, applied on the edge (face) ij. Perform the

needed integration by evaluating the integrand at the centroid of the element and treating the integrand as a constant

throughout the element.

For the rectangular element considered in Problem 10.52 and Fig. 10.35, find the element nodal force vector due to

an increase in the temperature of the element by 50 C. Perform the needed integration by evaluating the integrand

at the centroid of the element and treating the integrand as a constant throughout the element. Assume a plane stress

condition for the element

For the element described in Problem 10.36, determine the element nodal force vector as a result of the following prestress: sxx0 ¼ 800 psi, syy0 ¼ 500 psi, and sxy0 ¼ 750 psi. Assume the element to be in a state of plane strain. (take any triangular element or write formula only).

For the element described in Problem 10.36, determine the element nodal force vector as a result of the following prestress: sxx0 ¼ 800 psi, syy0 ¼ 500 psi, and sxy0 ¼ 750 psi. Assume the element to be in a state of plane stress. (take any triangular element or write the formula only).

Consider a rectangular element in plane stress state with the geometry shown in Fig. 10.35. The element is made of aluminum with E ¼ 71.0 GPa and v ¼ 0.33 and has a thickness of 0.2 cm. Using the [B] matrix given in Problem 10.12 and the [D] matrix given in Eq. (10.15), find the element stiffness matrix using the relation

farmer is using a tandem disk harrow for primary tillage in a medium texture soil. The disk width is 6 m, the travel speed is 10 km, and the tillage depth is 20 cm. Estimate the drawbar power of a tractor required. Ignore any losses that occur during field operations

A circular shaft of 12 cm dia. is subjected to combined bending and twisting moments. The bending moment being three times the twisting moment. If the direct tensile yield point of material is 350 MN/m² and factor of safety on yield is 4, find the allowable twisting moment by     

a) Maximum principal stress theory

b) Maximum shear stress theory

At a point in a strained material, the intensities of normal stresses on two planes at right angles to each other are 35 N/mm² and 20 N/ mm² both tensile. They are accompanied by shear stress of 15 N/ mm². Find the principal planes and principal stresses. Find also maximum shear stress.