ENGINEERING SALES MANUAL SUGGESTED BRIDGE DESIGN
SECTION PAGE REVISION DATE
The following method can be used for design of support structures for MixPro agitators. This method goes into detail for bridge supports. supports. Similar methods methods can be used for flange mounts. mounts. The support structure for an agitator must meet two criteria: 1.
The suppo support rt must must be capab capable le of withst withstand anding ing the design design loads loads withou withoutt fail failure ure..
2.
The suppor supportt must must be suffic sufficien iently tly rigid. rigid. This This is is nece necess ssary ary to limit limit deflec deflectio tions ns of the agitat agitator or assembly. This takes two primary forms, twist and vertical deflection. This twist must not exceed 1/3°, the total vertical deflection in either beam must not exceed 1/16" per 10 feet of beam length.
The following shows how to apply the rigidity criteria and then the deflection criteria to determine the bridge structure necessary. This example assumes the following: - the bridge consists of two main beams running across the top of the tank and supported on rigid supports. - The agitator is centered between the beams and between the supports. 1.
Determ Determine ine the loads loads the bridge bridge must must supp support ort.. The loads loads for the agitat agitator or are shown shown in the upper upper left corner of the Certified Unit Drawing.
2.
Deter Determi mine ne the the beam beam separ separati ation on that that will will be used. used. This This is typic typicall ally y achie achieved ved by mat matchi ching ng up up of appropriate bolt locations locations on the beam with mounting bolt positions for the agitator. agitator. For initial determinations determinations the mounting bolt spacing can be used.
3.
Dete Determ rmine ine the the allo allowa wable ble defl deflec ecti tion, on, from from twi twist st,, in the the main main beams beams.. Unde Underr wors worstt case case loa loadi ding ng one beam will deflect upwards and the other downwards in a twisting action. In this case only half the beam spacing is used to calculate allowable deflection:
d = w/2 w/2 * s in(1/3°) in (1/3°) ,
where
d = beam deflection (inches) w = beam spacing (inches)
4.
Determ Determine ine the overal overalll leng length th of the beams beams betwee between n supp support orts. s. The suppor supportt str struct ucture ure for the bridge must also be sufficiently rigid such that the deflection limits for the agitator are not exceeded when it is included. In this example it is assumed that the supports are rigid and the only deflections are in the bridge.
5.
Determ Determine ine the force force appl applied ied to each each beam beam by by the the bendi bending ng mome moment nt suppli supplied ed in in the the desig design n loads loads.. In this case each beam will carry half the load:
F = M/w M/w ,
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where
F = force on beam (lbs) M = bending moment (lbs) w = beam spacing (inches)
Professional Mixing Equipment Inc. 22 Melanie Dr., Unit 10 Brampton, ON Canada L6T 4K9 Fax: (905) 790-5420 E-mail:
[email protected]
A 7.0 5 11/17/05
SECTION PAGE REVISION DATE
ENGINEERING SALES MANUAL SUGGESTED BRIDGE DESIGN
6.
Determine the moment of inertia required for the beams to resist twist. This can be accomplished by treating the beam as a “simple support structure”. The maximum deflection of such a structure is:
d = F*L³/(48*E*I) ,
where
d F L E I
= maximum deflection (in.) = force (lbs) = beam length (in.) = modulus of elasticity (psi) = moment of inertia (in 4)
E = 29,000,000 (psi)
For steel beams,
I = F* L³/(1.392 x 109*d) This is the minimum required to resist twisting. 7.
Determine the moment of inertia required to resist total vertical deflection. This can be accomplished by treating the beam as a “simple support structure” and applying all vertical loads. The maximum deflection of such a structure is: d
total
= d
d
weight
+ d bending + d
weight
= W/2*L3 /(48*E*I ),
beam
where
d W L E
I d bending = F*L 3 /(48*E*I) , d
4 = 5*b*L /(384*E *I) , where
beam
See section 6. d b L E
I
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= deflection (inches) = mixer weight (lbs) = beam length (inches) = modulus of elasticity (psi) = moment of inertia (in 4)
= deflection (in.) = beam weight (lbs/in) = beam length (in.) = modulus of elasticity (psi) = moment of inertia (in 4)
Professional Mixing Equipment Inc. 22 Melanie Dr., Unit 10 Brampton, ON Canada L6T 4K9 Fax: (905) 790-5420 E-mail:
[email protected]
A 7.1 5 11/17/05
ENGINEERING SALES MANUAL SUGGESTED BRIDGE DESIGN
SECTION PAGE REVISION DATE
For the initial calculation, beam weight is ignored. The calculation will need to be redone once a beam has been selected to ensure that deflection criteria is still met. This reduces the deflection equation to: d
total
d
total
For steel beams, Also,
= d
+ d bending
weight
= W/2*L 3 /(48*E*I) + F*L 3 /(48*E*I) E = 29,000,000 psi d = 0.0005208*L
(1/16" per 10 feet)
I = (W/2 + F) * L2 /(7.25 x 10 5) This is the minimum required to resist total deflection. 8.
Consult a beam catalog and determine which ones satisfy both moment of inertia criteria.
9.
Calculate the total deflection including the beam weight to verify that the selected beam meets this criteria.
10.
Check the beams selected to ensure that they satisfy stress level requirements for both the combined bending and downward loads, and the torque.
11.
Beams will still require cross bracing and support.
Configurations that differ from the one shown here will require different approaches. The end result remains the same. The bridge must be sufficiently strong to support the loads without deflecting more than 1/16" per 10 feet of span and sufficiently rigid such that the agitator does not deflect through an angle greater than 1/3°. This also applies to flanges.
Phone: (905) 790-5444
Professional Mixing Equipment Inc. 22 Melanie Dr., Unit 10 Brampton, ON Canada L6T 4K9 Fax: (905) 790-5420 E-mail:
[email protected]
A 7.2 5 11/17/05
