As mentioned in your other thread, there seem to be some issues with units conversion.Confusedbiomedeng said:Homework Statement
A round bar .125mm in diameter , is to be used as a beam. IF Youngs modulus For the material E=200x103N/mm2 and the stress due to bending is limited to 17.5N/mm2
A) Maximum allowable bending moment
B) the radius of curvature at the point of Maximum bending moment
Homework Equations
σ/y=m/i=E/R
Ina=πD4/64
The Attempt at a Solution
A) 17.5/(125/2)=M/1.1x107 Bending moment =3080000
Ina=1.1x107
B) 17.5/125/2=7/25
=> R= 7/25/200x103 R=1.4mm
That isn't quite what I asked for, but anyway...Confusedbiomedeng said:so for allowable bending moment i took the stress 17.5 N/mm2 and divided it by 125/2 assuming neutral axis to be down the centre which gave me and answer of 7/25 this was then equal to m over π(1254 )/64which is the equation for moment of inertia, that was an answer of 1.1x107. to get M alone i multiplied both sides by 1.1x107 giving 308x104 N/mm4 since in the question the values are given in terms of mm i left the diameter in mm.
and for B) again I put stress over neutral axis and got 7/25 put that equal to 200x103 over R. To get R alone i divided both sides by 200x103 to get R out as 1.4mm
does this answer your previous question.
I still do not understand this line. Your quoted equation is that σ/y = E/R, but you seem to have done R=(σ/y)/E. Further, I do not understand how 0.28/(200x103) gives 1.4. Shouldn't it be 1.4x10-6? Since you believe you have standardised on mm as the unit of distance, there should be no final units conversion.Confusedbiomedeng said:> R= 7/25/200x103 R=1.4mm
A maximum bending moment is the point along a beam where the internal stresses are at their highest, causing the beam to potentially fail under excessive load.
Maximum bending moment is calculated using the formula M = WL/4, where M is the maximum bending moment, W is the total load applied to the beam, and L is the length of the beam.
The radius of curvature for a round beam is the distance from the center of the beam to the point where the beam begins to curve.
The radius of curvature for a round beam is calculated using the formula R = M/EI, where R is the radius of curvature, M is the maximum bending moment, E is the modulus of elasticity, and I is the moment of inertia of the beam.
It is important to calculate maximum bending moment and radius of curvature for a round beam in order to ensure that the beam can withstand the expected load without failing. These calculations also help engineers determine the appropriate size and shape of the beam for a given application.