Deisgn of Steel Hopper for Impact Loads 3

Is that the method described in Blodgett’s Design of Welded Structures, where the potential energy of the falling object is equated to the energy that can be absorbed elastically by the member in bending? The equations look similar.

A couple of questions:
- Does the bin have a grizzly (grillage of steel beams) over the opening? If so, what is the aperture? If so you may be able to reduce the drop height and potential energy for objects with diameter equal to 100% of the aperture and assume that an objects with diameter up to 80% of the aperture pass through without losing any energy by hitting the grizzly.
- Is the object large enough for you to distribute the impact over a two stiffeners?

Some design guidelines (written by mining and minerals processing companies) simply require that you increase the design pressures by 100% to account for severe impact loading. Have you checked if your Client has a standard design guideline for bins and silos?

ShaunB,
I have several design manuals that regard your situation. One is Gaylords Design of Steel Bins, and Troitsky Tubular Steel Structures from the Lincoln Arc Welding Foundation. In Troitsky's book chapter 7 is on the design of bins and bunkers. For dynamic loading in bunkers he recommends the following (Table 7.6) which gives a Cd value for the design pressure, based on Pdes = Cd*P, where P is the calculated static pressure. The chart gives the following values of Cd.
(Ratio of volume dumped in
one load to total bunker
capacity)
Cd (Dynamic Coefficient)
1:2 ------------------------>> 1.4
1:3 ------------------------>> 1.3
1:4 ------------------------>> 1.2
1:5 ------------------------>> 1.1
1:6 and less --------------->> 1.0

I have used these values with positive results in the past. I agree that you can use an energy approach, and probably that would be the most exact approach. The problem is that it is really hard to determine exactly how the ore will hit the bunker wall, where it will hit, how it will distribute the load, and what effects the whole 240 ton truck load will have. What happens when a rock falls and impacts the wall, and at almost the same instant another rock hits next to it, or on top of it. Also, as dbuzz mentioned, a grizzly will take a lot of velocity out of the large rocks and reduce the impact loads. As a side note, you may approach your client with a design which utilizes a rock on rock hopper. What this essentially will be is a flat bottom hopper, with a hole in the floor wherever the discharge is desired. If made large enough and designed properly, you will end up with a cone hopper, with 45 degree side walls made of stone, and they can absorb all of the impact from the falling stone. It's the best way to handle falling stone impact loads, and the impact transferred to the walls is minimal. It also keeps your client from having to replace hopper wall plates, because they won't see the wear, like they would with a stone on plate design.

I am suprised that your calculations give forces as small as 1000 kN. If you make the stiffeners stronger, they get stiffer and so deflect less and so (assuming your analysis is as per Blodgett), the force increases. It is a never ending cycle.

What does your theory say about the effect of the reduced stiffness if the design rock lands at a corner of the hopper? Again the deflection tends to zero, so the impact force tends to infinity.

Note that the liners will often not align with the stiffners in which case they will not protect the platework from rock impact - consider a rock that hits the unsupported corner or edge of a liner.

Hoppers platework, stiffeners, grizzlies and support beams do fail from rock impact. I would suggest caution before accepting a low impact force.

The above comments may all be irrelevant. Are you aware that when they start up the hopper for the first time, they will put sand or gravel in it, and thereafter they will use level detectors to keep material in it during operation in order to protect the apron feeder from rock impact? The problem here is that you cannot calculate the impact force as you do not know the stopping distance of the rock.

The formula I used was taken from Solutions to Design of Weldments (D810.17) - Lincoln Electric Company 1991. In fact there is an example given for a 100lb rock hitting a bumper plate assembly which is very similar to the problem I have at hand.

The use of a grizzly to reduce the height of fall and the size of the lump hitting the stiffeners has been suggested to the Client. Infact there are similar dump hoppers for this Client on other sites which do include a grizzly. The Client has advised us "that this bin does not need a grizzly, because the ore is much softer than the other sites". The problem I have is how to quantify the amount of deformation in the lump which increases the deceleration distance and hence reduces the impact force.

The shell is protected by impact rails (free issue from the Client) which run at right angles to the main horizontal stiffeners. They are at 180mm centres and so after a short time the gap between them is filled with ore so you end up with a composite steel/ore liner which protects the shell. Obviously this will assist in sharing the impact loads to the other stiffeners but again this is almost impossible to quantify.

AS3774 - the Australian Standard for loads on bulk solids containers contains similar guidelines to those mentioned by dbuzz and aggman whereby the normal/friction pressures are increased by an impact load coefficient. I was not sure that this was intended to be used for discrete lumps. I will try and chase up someone on the Code Committee regarding this.

PXC, you are correct in saying that the stronger the stiffener the higher the impact load. I have looked at a lump hitting the midspan of the stiffener and assessed the stiffener stresses for a trial section. The stresses reduce as you increase the stiffener size, however the impact load increases. Eventually you can converge on a solution. As the rock impact position moves closer to the corner of the hopper the impact load increases (since deflection reduces) however the bending moment reduces and hence stresses in the stiffener reduce. And yes the apron feeder will be protected from high impact loads since there is always a "dead" volume of ore in the hopper at all times.

Thanks very much for your help and comments guys.

The impact rails (some sort of railway material?) run orthogonal to the main stiffeners and are very closley spaced (180 CRS).

They will be very stiff and will spread the impact load across multiple stiffeners. I don't think you need to be too worried - but of course you need to do the numbers to prove it.

Are you designing the stiffener for the relevant component of the kinetic energy? As you know, the rock will continue on its downward path after striking the wall and deflecting. Most design examples have a horzointal beam completely arresting the vertical motion of a dropped object, which isn't the case here.