Pure bending of reinforced concrete example #1

[@jammingchords4856]

I is wrong ,

[@Engineer4Free]

Yes unfortunately there is a math typo in this video. The process is correct, but the typo unfortunately happened and carried through to make I and the end result incorrect.

[@francosfusion]

@@Engineer4Free What is the right answer?

[@patrickmoseley8865]

@@francosfusion When I calculated it. I got I = .0013623 m^4, compressive stress = 24.4 kPa, and tensile stress = 333.3 kPa

[@austinmeredith6647]

Your moment of inertia is wrong. Ix= 1.362*E-3 m^4.

[@morganoconnor4486]

Awesome video. This made this topic transform from very fuzzy at best from the textbook explanation to crystal clear. Thanks!

[@Engineer4Free]

Amazing!! Glad I could help ya 😁😁

[@alexadusei5318]

Please why is the moment of inertia about the neutral axis for the rectangle not 1/12 bx^3

[@sudhanshunain4690]

that is about the axis passing thru center.

[@mybluebucket2630]

One term is missing in Ixx. 1/12 nb*(As/b)^3

[@danishkhadim4048]

NAs =no of steel rod×area of rod×Es/Ec ratio ? Is this right

[@francosfusion]

How did you obtain the moment value of 200Nm?

[@1224davdavid]

Is there an error in your Ix? I got 1.36197e-3 m^4.

[@simonchege287]

I got that too for I

[@nathanmakando8058]

This is good material. Can you advice a reference book with more calculations and problems (metric units). Thanks

[@Engineer4Free]

Thanks Nathan! Yeah there's a pretty good textbook and also practice problem book that I link to in the side bar of engineer4free.com/mechanics-of-materials check them out!

[@Maurovers]

I always like when people give me a concrete example in engineering

[@Engineer4Free]

😏

[@sidneynjau7907]

😂😂😂😂nice

[@philipjovelolesco3754]

Omg.. this is so helpful. Thank you so much

[@kussaialraini4872]

is it just me or did you not, include the cube and the square, while calculating the Moment of inertia...

[@anesmerazi603]

sir why is the neutral axis not in the middle of the cross section .ie. d/2 ?

[@Engineer4Free]

Because the steel and concrete do not have the same modulus of elasticity. When we transform the steel to an equivalent area of E=25GPa and then ignore the concrete in tension, the cross sectional area that we are working with is no longer rectangular. I recommend watching videos 29-34 here: engineer4free.com/mechanics-of-materials and if you have time, videos 22-28 also lead into those and would be helpful background information. Neutral axis is only d/2 for members that are symmetrical about the axis.

[@israelcrawford8734]

If i create a FE model of rein. concrete can I use this calculation to validate my model ?

[@Engineer4Free]

This method is from Beer and Johnston Mechanics of Materials, you can check this software too bit.ly/skyciv-e4f they have a reinforced concrete calculator under the "software" tab in the top navigation menu.

[@israelcrawford8734]

@@Engineer4Free thanks Sir

[@재드래곤-w3v]

very useful *thankyou*

[@Engineer4Free]

Thanks for watching! =)

[@jephassinkala9672]

why are u using nAs instead of (n-1)As

[@Engineer4Free]

If you define n as the ratio of (the original modulus of elasticity of the section you want to transform) divided by (the modulus of elasticity that you are transforming it to), then you will be virtually increasing or decreasing the transformed section by that value when we multiply it by n. In this case n=Es/Ec gives us a value greater than one (8). It's like saying the steel is worth 8 times more than a material of E = 25 GPa, so if we transform it to an equivalent area of a material with E = 25 GPa, then the transformed area = n(As) = 8(As). I'm not familiar with a method that would use (n-1)As, if there is one, perhaps they are defining n differently. Did you watch the previous video? If not you can see it here: engineer4free.com/4/pure-bending-of-composite-materials-introduced hopefully the explanation there clears up the method that I follow in this video!

[@SydneyRover]

The (n-1)As is used when the concrete below the N/A is not removed from the equation, in other words for an uncracked section. When the section is fully cracked, then nAs is used instead.

[@islemekrani597]

thank you so much for your benefical videos :)

[@Engineer4Free]

You're welcome, thanks for watching!! 🙂

[@simonchege287]

I got that too for I

[@israelcrawford8734]

Thank you Sir

[@Engineer4Free]

You’re welcome, thanks for watching!! 🙂

[@israelcrawford8734]

@@Engineer4Free quick question if i may, i am using this calculation to calculation bending stress in a beam for an Finite element concrete beam, so you know if this is the correct calculation ?

[@aminarahmanraisa9119]

Sir why it's 1/3 bx^3 not 1/12 bx^3

[@Engineer4Free]

It's a shortcut when the axis of interest is on the edge of the rectangle you are concerned with. If you write 1/12 bx^3 it will actually sinplfy to 1/3 bx^3 so you can just skip the simplification if you know recognize the scenario. You can see both 1/12 and 1/3 variations listed here: en.wikipedia.org/wiki/List_of_second_moments_of_area