Calculating the Required Section Modulus for a 200mm Wide Flange Beam

[joemama69]

Homework Statement

A simple beam of length L = 5m carries a uniform load of intensity q = 5.8kN/m and a concentratexd load 22.5kN. Assuming stress allow = 110MPa, calculate the required section modulus S. Then select a 200mm wide flange beam (W shape) from the table. recalculate S taking into account the weight of the beam. select a new 200mm beam if neccessary.

Homework Equations

The Attempt at a Solution

Of first I was trying to calculate the M_max and i made a boo boo somwhere.

First I found the Moment about A

0 = 5.8(5)(2.5) + 22.5(3.5) - 5R_B... R_B = 30.25kN

About B

0 = 22.5(1.5) + 5.8(5)(2.5) - 5R_A... R_A = 21.25kN

Then so determine the Maximum Moment I was preparing the Shear & moment graphs. I took x starting from the left where x = 0 @ A

0<x<3.5

Force sum in y = 0 = R_A - qx - V... V = 21.25 - 5.8x
Sum of M = 0 = R_Ax - qx²/2 - M... M = 21.25x - 2.9x²

3.5<x<5

Force in y = 0 = R_A - qx - P -V... V = -1.25 - 5.8x
Sum of M = 0 = R_Ax - qx²/2 - 22.5(x - 3.5) - M... M = 78.75 - 1.25x - 2.9x²

when I graph the V's, the lines do not intersect... did i do something wrong. Would it even matter as long as I did the M's correctly. Could someone just double check my work.

 

[PhanthomJay]

Your equations look OK. Max moment occurs at point of zero shear. Draw a shear diagram. There is an abrupt change in shear at the applied concentrated load. If you plot your 2 shear equations, they won't intersect at a common point because of the concentrated load discontinuity.

 

[joemama69]

ok i found V = 0 @ x = 3.664

So pluged this into the second M equation and got M_max = 35.7kN*m

S = M/$$\sigma$$ = 3.25X10^-4 what happened here

 

[PhanthomJay]

Your numbers are off a bit...point of zero shear ocurs at the concentratd load at x =3.5 m. M_max at that point is about 40 kN-m. Then when you calculate S, the result is in m^3. (i don't work in SI units, so i don't have a feel for the numbers)

 

[DeeNos]

I would suggest going back and checking your calculations to ensure that you have not made any errors. It is important to have accurate values for the reactions and maximum moment in order to properly calculate the required section modulus. Additionally, I would recommend using a more systematic approach to solving the problem, such as using the method of sections or the moment-area method. This will help to avoid any mistakes and provide a more accurate solution.

Once you have confirmed your values, you can use the equation S = Mmax / (allowable stress) to calculate the required section modulus. From there, you can refer to the table of standard beam sizes to select a 200mm wide flange beam with a sufficient section modulus.

Taking into account the weight of the beam will change the reactions and therefore the maximum moment, so it is important to recalculate these values before selecting a new beam if necessary. It may also be helpful to consult a structural engineering handbook or software to ensure that the selected beam is appropriate for the given loading conditions.