How Does Material Heterogeneity Affect Beam Stress Analysis?

[Dell]

for the folowing beam made up of a top half where E=210Gpa and a bottom part where E=70Gpa a=0.2m t=0.024m, b=0.04m

i am asked a few different things


a)to find the shear forces and bending moment arrays in the beam

b)plot the normal stress as a function of the moment,

how do i do this? surely the normal stress is a function of Y, otherwise i would just use "sigma=-y*M/I" i have already found I so assuming i found the correct I i would just have a linear graph with a slant of -y/I
is this correct?? is this a common thing to be asked, i have only ever seen sigma plotted against y ?

c) given that P=1KN, find the shear flow at points a,b ??
is shear flow not only for torsion?? is there torsion in this problem if the forces P are applied at the center of the top of the bar-pure bending-?? is this a trick question??

d) will the size of the shear strain at these points a,b change if the bar is turned upside down??
again, are there shear strains in pure bending? i think not??

 

[KataKoniK]

a) To find the shear forces and bending moment arrays in the beam, you will need to use the equations for shear force and bending moment. These equations are:

Shear force: V = Q - P, where Q is the distributed load and P is the point load.

Bending moment: M = Qx - Px, where x is the distance from the point of interest to the end of the beam.

Using these equations, you can calculate the shear force and bending moment at different points along the beam.

b) To plot the normal stress as a function of the moment, you will need to use the formula sigma = -y*M/I, where y is the distance from the neutral axis and I is the moment of inertia. As you mentioned, this will result in a linear graph with a slope of -y/I. This is a common thing to be asked and is used to analyze the stress distribution in a beam under bending.

c) Shear flow is indeed related to torsion, but it can also occur in beams under bending. In this problem, the shear flow can be calculated using the formula q = VQ/I, where V is the shear force, Q is the first moment of area, and I is the moment of inertia. The shear flow at points a and b can be found by plugging in the appropriate values.

d) Shear strains do not occur in pure bending, so the size of the shear strain at points a and b will not change if the beam is turned upside down. However, if the beam is subjected to a combination of bending and torsion, the shear strains may change when the beam is turned upside down.

 

[Mene]

a) To find the shear forces and bending moment arrays in the beam, you will need to use the equations for shear force and bending moment. The shear force equation is V=Q/A, where V is the shear force, Q is the applied load, and A is the cross-sectional area of the beam. The bending moment equation is M=Qx, where M is the bending moment, Q is the applied load, and x is the distance from the point of interest to the applied load. You will need to calculate the shear force and bending moment at each point along the beam and create an array or table to organize the data.

b) To plot the normal stress as a function of the moment, you will need to use the equation sigma=-y*M/I, where sigma is the normal stress, y is the distance from the neutral axis, M is the bending moment, and I is the moment of inertia. You will need to calculate the normal stress at different points along the beam and plot them against the corresponding bending moment values. This will give you a curve that represents the variation of normal stress along the beam.

c) Shear flow is not only for torsion, it is also present in beams subjected to transverse loads. In this problem, you will need to use the equation q=VQ/I, where q is the shear flow, V is the shear force, Q is the applied load, and I is the moment of inertia. You will need to calculate the shear flow at points a and b using this equation and the values for V and Q given in the problem.

d) In pure bending, there is no shear strain present. Therefore, the size of the shear strain at points a and b will not change if the bar is turned upside down. Shear strain only occurs in beams subjected to shear or torsion forces.