Bending Force calculation on Reinforced bar bundles

[AiyushG]

Hi,
I need to calculate the Bending Force required to bend a reinforced bar bundle.

The bundled bar is in 12M in length with each individual bar having a diameter of 32mm having 15 Bars in the bundle which weighs approx 1136 kg. The yield strength is 650 MPa.
How to calculate the bending force when it's a bundle and not a single bar

Need some help formulating and calculating it

 

[Stress_Eng]

Could you supply a picture of the cross section and explain how they are joined together. Also a FBD would be informative.

 

[AiyushG]

They are tightly Bundled using steel straps at the manufacturing units. Making an outer circle of large diameter containing 15 smaller circles of 32 mm dia

 

[HTURKAK]

What is dictating the behavior of the bundle with 15 Bars is a compound section?
If only some friction provided , assuming each bar is separate beam will be safe and reasonable approach.

 

[AiyushG]

They are bundled at multiple points about 9-10 straps. Making them to be considered as a compound section i guess. Yes, there's friction for sure as they are ribbed bars used for construction.

 

[AiyushG]

Is it a right approach to consider actual area covered by the bars i.e. N×(pi*d^2)/4 then the cumulative diameter shall be sqrt(N×d2)

Assuming them as a compound bar, calculating bending moment
M = Yst × I / c

 

[phamENG]

Not to be that guy, but aren't student posts supposed to be limited to the student forum?

 

[GregLocock]

The required bending moment for fully plastic deformation will be somewhere between 15 times the moment of plasticity ((d^3/6)*yield_stress) of a single bar, and that of the entire cross section, which would be about 3 times bigger.

But the bundle will be permanently bent once the outer fibres yield.

 

[HTURKAK]

Is it a right approach to consider actual area covered by the bars i.e. N×(pi*d^2)/4 then the cumulative diameter shall be sqrt(N×d2)

No..
It is true that the total area of the bars = N×(pi*d^2)/4
If you want to find the MOI of the assembly section, ( probably hexagonal) you must apply paralel axis theorem.

 

[Stress_Eng]

The minimum inertia based on the possible stack arrangement and rotation position should be used.

 

[GregLocock]

An alternative estimate for initial yield would be to use M/I=s1/y

where s1 is the yield stress times the 'fullness' of the bundle.

My /guess/ is the bundle will act as a single bar in bending, and that's the upper bound on M.