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1. Define the load cases that must be considered. For this purpose, use the British Standard BS EN 1991-3:2006 (retrieve it using the iCAT service of our University).
2. Find the position of the trolley for which the bending moment is maximized
3. Plot the bending moment diagram for the bridge girder
4. Find the position of the trolley for which the shearing force is maximized
5. Plot the shearing force diagram for the bridge girder
6. Find the position of the trolley for which the vertical deflection is maximized
7. Plot the deflection diagram for the bridge girder
8. For the defined load cases and the selected positions:
o Estimate the corresponding stresses
o Check adequacy with respect to the constraints.

## Design Data Considered

An Overhead Traveling (OT) crane or rather commonly referred to as ‘bridge crane’ is normally configured by having parallel runways such that the gap between the rails is spanned by a horizontally traveling bridge. The degree of freedom is restricted only in the x-y plane such that the bridge moves in the longitudinal direction. The crane has got a hoist which does the lifting of objects via electrically excited system. The trolley therefore moves horizontally on the beam bridge. Admittedly, these crane types have found wide applications in various industries such as shipping, machining and other industrial stations and whose major functionality is to lift and move heavy objects like wheels of bogies among others. For instance, in the rolling stock industry, the OT crane is used to facilitate replacement of old wheel and axles of bogies (Globalspec.com, 2018). The bridge is normally built using either plate welding or hot rolling of steel (Cranes, 2018). However, most of commercially available steel material comes from hot rolling which itself is an opportunity to provide sufficient structural integrity of the bridge. The strength of the beam must be adequate to carry the live and dead loads and endure the various stresses as the system is in operation (Directindustry.com, 2018).  Therefore, hereinafter, a major design to size and select the dimensions of the bridge girder ensues. This is a preliminary design and analysis report whose aim is to: undertake the design calculation and illustrate N-Q-M diagrams by applying the singularity-functions methods and the equivalent stress techniques; then we base it in a real-life engineering application (Mathalino.com, 2018).

Notably, for the purpose of design constraints, we consider the following standards: BS EN 1991-3:2006 and BS EN 1993-6: 2007.

Consider the following given design data for the system:

Table 1: Given Design Data

 PARAMETER VALUE Crane bridge span 6m Lifting capacity 3.2tn Trolley wheel base 600mm Trolley Load distribution 40-60%, end beam approach at 100mm (on both sides)

The system must operate within defined limits. Therefore, the following are the given constraints that define the operational limits:

• Maximum vertical displacement: 20mm or span/600 (whichever is smaller)
• Maximum developed stress: less than yield stress
• Partial Factor Of Safety (applied on yield stress): 1.15
• Fundamental frequency: greater than 1.2Hz

In the given system, the following are the assumptions that have been made to facilitate design of the crane system:

• The bridge girder is considered simply supported beam
• The loading is uniformly distributed but with varying positions along the rail , check figure 2 for the free body diagram of the load system (Brighthub Engineering, 2018)
• Lifting capacity is inclusive of the trolley weight and the hoist
• Cables and festoon pushbutton  are of negligible weight

Defining the load cases being considered

For this purpose, we use the British Standard BS EN 1991-3:2006 (Shop.bsigroup.com, 2018). The provided standard designates the loading arrangement which is adopted in the system.

Finding the position of the trolleyfor which the bending moment is maximized

From the given data, we know that the rail shares the load in the ration of 40 to 60% hence correspondingly R1 and R2 are determined:

## Design Calculation and Analysis

R1= 0.4x31.4= 12.56kN

R2= 0.6x 31.4= 18.84kN

Next, we find the reactions at supports A and B shown in the FBD figure 2

Given the system is at static equilibrium such that:

Ray+Rby=R1+R2=Qr and with a little consideration from the FBD we see that the reactions are actually sharing the load equally hence: R1=R2= Qr/2= 31.4/2=15.7kN

We then find the Bending moment equation by considering moments about A:

Ma= -12.56x-18.84(x+d1)+15.7x6

= -12.56x-18.84x-18.84d1)+94.2

Ma= -31.4x +82.896….(i)

For the position of maximum bending moment, we put equation (i) as being equal to 0 hence:

-31.4(x) +82.896= 0;    -31.4x=-82.896, x= 2.64 (that is 2.64m from point A)

Plot of the bending moment diagram for the bridge girder

 X BMx 0 82.896 1 51.496 2 20.096 3 -11.304 4 -42.704 5 -74.104 6 -105.504

Figure 3: Bending moment diagram

Finding the position of the trolley for which the shearing force is maximized

For shear force, we set Vx  +ve

Hence Va= 31.4-15.7= 15.7kN (shear force is constant all over the beam)

Plot of the shearing force diagram for the bridge girder

 Shear force diagram (15.7kN) x Vx 0 15.7 1 15.7 2 15.7 3 15.7 4 15.7 5 15.7 6 15.7

Figure 4: Shear force diagram

Finding the position of the trolley for which the vertical deflection is maximized

For Maximum Deflection, we use the double integration method as follows (Hsu, Weng and Yang, 2014):

From this expression: EId2y/dx2 = M = -31.4x+82.896 we integrate it to obtain the slope:

Hence:   EIdy/dx=-31.4x2/2+82.896x

EIdy/dx=-15.7x2+82.896x+C1

The boundary conditions: dy/dx=0, when x=0

0= -15.7(0)2+82.896(0)+c1, C1= 0

Hence EIdy/dx= =-15.7x2+82.896x…. (ii)

Further integrating equation (ii) to obtain the deflection:

EIy =-15.7x3/3+82.896x2/2+C2…. (ii)

EIy= -5.23x3+41.448x2+C2

Again invoking the boundary condition: at x=0, y=0

Substituting in (ii):

0=-5.23(0)3+41.448(0)2+C2

0= +C2

Hence the slope equation: dy/dx =-5.23x3+41.448x2… (iii)

For maximum deflection, we differentiate or rather we pick the slope equation (ii) and equate to zero hence:

EIdy==-15.7x2+82.896x=0

X(82.896-15.7x)= 0

X=0, or x=-82.896/15.7=5.22

We take the latter as it is more practical considering the system in figure 2 hence position is at 5.22m from point A

2.4.7 Plot of the deflection diagram for the bridge girder

 x y 0 0 1 36.218 2 123.952 3 231.822 4 328.448 5 382.45 6 362.448

Figure 5: Deflection equation diagram

For the defined load cases and the selected positions:

(a) Estimating the corresponding stresses

First we need to go back to the position at which maximum deflection occurs hence x=5.22 is the position and we substitute in the bending moment equation:

M= -31.4(5.22)+ 82.896= -81.012kNm

Now we need to size the beam hence from this expression, we can get the moment of Inertia I (Codecogs.com, 2018):

## Selection of Girder Bridge Profile

M/I=E/R

I= MR/E

Taking E= 203GPa and R= 300/2=150mm (neutral axis)

I= 81.012 x 0.15/203x109= 5.986x10-11m4

Fixing b at 0.3, d can be found since we know: I= bd3/12 (assume rectangular section)

Hence d= {(12x 5.986x10-11)/0.3}1/3= 1.338m

Now, Ax= 6x 1.338= 8.028m2

And Az= 0.3 x 6= 1.8m2

Hence:

Local shear stress τ,Ed

= Qr/Ay= 31.4/(0.3x 1.338)= 78.226MPa

Longitudinal stress σx,Ed

= Qr/Ax= 31.4/1.8= 17.44MPa

Traverse stress σz,Ed

= Qr/Az= 31.4/8.028= 3.911MPa

Yield stress fy

=200MPa, fy/Ym= 200/1.15= 173.91MPa

(b) Checking adequacy with respect to the constraints.

Note: we check the Ultimate Limit State of the bridge girder using the following equation:

Where:

σx,Ed: design value of the local longitudinal stress at the point of consideration

σz,Ed: design value of the local transverse stress at the point of consideration

τEd: design value of the local shear stress at the point of consideration

fy: yield stress for the selected material

γMo: partial factor of safety

We substitute the respective values in the above expression of constraints:

Let us break into terms:

(ρx/f/γ)2= (17.44/173.91)2= 0.010056

(ρz/f/γ)2 = (3.911/173.91)2 = 5.057x 10-4

(ρz/f/γ) (ρx/f/γ)= 0.10028x0.02248= 4.4609

3(τ/f/γ) = 3(78.226/173.91) = 0.6069

Checking by substituting in the above expression of constraint:

=0.010056+ 5.057x 10-4-4.4609+ 0.6069= -3.843<1

Hence the design is safe

Based on the design output and using a theoretical approach, we undertake a selection of a girder bridge profile. It must meet the given design specifications and be of minimum weight.

From Harrington hoists catalogue (Qu et al., 2014), we select the bridge girder: S15x42.9 with a capacity of 6.1m span and capacity of 3 to 5 tones

Conclusion

From the foregoing, we can conclude that the design output and the selected commercially available bridge girder match (bridges, 2018). In the calculation, a capacity of 3.2 ton and span of 6m was used to design the system by considering the structural integrity of the bridge girder. From checking of structural constraints, it has been established that the design is safe (Makeitfrom.com, 2018). However, it should be noted that the design did not consider various operational parameters like fracture toughness among others. The calculations only assumed static conditions. Therefore, in future design work of overhead travelling crane, dynamic conditions will have to be considered so that the loading system can aptly be established. Otherwise, as far as the given constraints are concerned, this design is safe and will operate sufficiently with minimum break downs.

References

Alibaba.com. (2018). Overhead Travelling Crane Design, Overhead Travelling Crane Design Suppliers and Manufacturers at Alibaba.com. [online] Available at: https://www.alibaba.com/showroom/overhead-travelling-crane-design.html [Accessed 24 Feb. 2018].

bridges, E. (2018). EN 1991-2: Eurocode 1: Actions on structures - Part 2: Traffic loads on bridges : European Committee for Standardisation : Free Download & Streaming : Internet Archive. [online] Internet Archive. Available at: https://archive.org/details/en.1991.2.2003 [Accessed 24 Feb. 2018].

Brighthub Engineering. (2018). Design Guide for Overhead Cranes. [online] Available at: https://www.brighthubengineering.com/machine-design/67436-overhead-travelling-crane/ [Accessed 24 Feb. 2018].

Codecogs.com. (2018). Moments of Inertia - Bending Stress - Materials - Engineering Reference with Worked Examples. [online] Available at: https://www.codecogs.com/library/engineering/materials/bending_stress/moments-of-inertia.php [Accessed 24 Feb. 2018].

Directindustry.com. (2018). Single-girder overhead traveling crane / with hoist / large - Zero Emission V - Demag. [online] Available at: https://www.directindustry.com/prod/demag/product-14949-1878156.html [Accessed 24 Feb. 2018].

Globalspec.com. (2018). Overhead Bridge Cranes | Products & Suppliers | Engineering360. [online] Available at: https://www.globalspec.com/industrial-directory/overhead_bridge_cranes [Accessed 24 Feb. 2018].

Hsu, M., Weng, T. and Yang, D. (2014). Dynamic Teaching on the Deflection Determining of Beams. Advanced Materials Research, 889-890, pp.1700-1703.

Makeitfrom.com. (2018). Hot Rolled 1010 Carbon Steel :: MakeItFrom.com. [online] Available at: https://www.makeitfrom.com/material-properties/Hot-Rolled-1010-Carbon-Steel/ [Accessed 24 Feb. 2018].

Mathalino.com. (2018). Double Integration Method | Beam Deflections | Strength of Materials Review. [online] Available at: https://www.mathalino.com/reviewer/mechanics-and-strength-of-materials/double-integration-method-beam-deflections [Accessed 24 Feb. 2018].

Qu, X., Xu, G., Fan, X. and Bi, X. (2014). Intelligent optimization methods for the design of an overhead travelling crane. Chinese Journal of Mechanical Engineering, 28(1), pp.187-196.

Shop.bsigroup.com. (2018). BS EN 1991 - Eurocode 1 : Actions on structures. [online] Available at: https://shop.bsigroup.com/Browse-By-Subject/Eurocodes/Descriptions-of-Eurocodes/Eurocode-1/ [Accessed 24 Feb. 2018].

Cite This Work

"Design And Analysis Of Overhead Traveling Crane Bridge Girder." My Assignment Help, 2020, https://myassignmenthelp.com/free-samples/me5011-thermofluids-and-mechanical-systems-for-overhead-traveling.

My Assignment Help (2020) Design And Analysis Of Overhead Traveling Crane Bridge Girder [Online]. Available from: https://myassignmenthelp.com/free-samples/me5011-thermofluids-and-mechanical-systems-for-overhead-traveling
[Accessed 06 August 2024].

My Assignment Help. 'Design And Analysis Of Overhead Traveling Crane Bridge Girder' (My Assignment Help, 2020) <https://myassignmenthelp.com/free-samples/me5011-thermofluids-and-mechanical-systems-for-overhead-traveling> accessed 06 August 2024.

My Assignment Help. Design And Analysis Of Overhead Traveling Crane Bridge Girder [Internet]. My Assignment Help. 2020 [cited 06 August 2024]. Available from: https://myassignmenthelp.com/free-samples/me5011-thermofluids-and-mechanical-systems-for-overhead-traveling.

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