Week 11 Challenge

Aim: To determine the temperature load acting on bridge and analyze accordingly in Staad.Pro.

Introduction:

The objective is to calculate temperature loads from the given data manually and attempt the same in Staad.Pro for the bridge and analyse the results and effects on the structure.

The Illustrated bridge is 9.0 m long in length and width of 7.0 m having cantilever of 0.5m. And Box girder is provided to support the deck slab.

Given Data (for calculation):

Span of bridge = 9.0 m

Width of carriage way = 7.0 m

Number of Main Girders = 3

Location = Delhi

Diameter of pier = 2.5 m

Width of Pier cap = 6.0m

Thickness of deck slab = 550 mm = 0.55 m

Size of Box girder = 1.5 m x 1.5 m and thickness of web = 0.3 m

Compressive strength of concrete = 40 N/mm²

Assumption:

Size of Pier Cap = Parallel side as 3.25 m & 2.5 m and Depth as 1.1 m.

Ignoring the self-weight of structure.

Procedure:

All the dimensions are taken from the center line of section of different element of bridge, as shown in figure below,

Height of Pier = 10.0 + 1.1 = 11.1 m

All the loads are calculated in such a manner as mentioned below,

Maximum temperature at Delhi C.H.O. as per IRC 6 2017 = 47.8^o C

Minimum temperature at Delhi C.H.O. as per IRC 6 2017 = -0.4^o C

Effective temperature difference (T_eff) = [(47.8 - (-0.4))/2] + 10 = 34.1 ^o C

Coefficient of Thermal Expansion (α) = 12.0 x 10^-6/ ^o C

Young Modulus of concrete (E) as per IS 456 = 5000√fck = 5000 x √40 = 31622.777 KN/m²

Stress due to Temperature (σ_temp) = α x T_eff x E = 12.0 x 10^-6 x 34.1 x 31622.777 = 12.94 KN/m²

Maximum Permissible Stress (σ_perm) = (2/3) x 0.7 x √fck = (2/3) x 0.7 x √40 = 2.952 KN/m²

Hence, Stress is restricted to 3 KN/m².

Positive Temperature Differences:

Temperature at top of deck = 47.8 ^o C

Temperature at bottom of deck = (2.1/17.8) x 47.8 ^o C = 5.64 ^o C

Reverse Temperature Differences:

Temperature at top of deck = 47.8 ^o C

Temperature at bottom of deck = (6.6/10.6) x 47.8 ^o C = 29.762 ^o C

Computer Proficiency:

1. Create a model by putting the necessary inputs as file location, units etc.

2. Create two nodes (x,y,z) represents as (0,0,0) & (0,11.1,0) Because the height of pier is assumed to be 11.1 m.

3. Go to Add Beams option and connect the both nodes.

4. Select the top node of pier and replicate to the -3.0 m & 3.0 m in z direction. Connect the beam at the top of pier by add beams option in order to make pier cap.

5. Replicate the whole assembly to 9.0 m in x direction. And connect the pier cap with beams in order to make box girder beam.

6. Go to Properties tab, define the size of piers, Pier cap & Box girder beam as mentioned above and assign all the members accordingly.

7. Go to supports tab, and create fixed support and assign to end of piers.

8. Select the end nodes of pier cap and replicate the node at 0.5 m distance both side of pier caps in order to make cantilever.

9. Assign all the missing property element as discussed above. Refer image below.

10. Go to create mesh, and connect corner node of the panel and create quadrilateral mesh of 0.5 m x 0.5 m.

11. Provide the number of divisions to each side of panel for creating mesh.

12. Assign the thickness of the plate and replicate it into every panel in order to make deck slab.

13. Go to the Material tab, Select edit button for concrete, and provide the compressive strength of 40000KN/m2. As grade of concrete is provided as M40.
14. Go to loading tab, define the temperature load as discussed above and assign to the deck slab of bridge. Refer image below.

14. Add another load case for reverse temperature load as per IRC 6. And assign the load to the plates of deck slab. Refer image below.

15. Add a load combination for temperature load with the factor of 1 for Analytical results. Refer image below.

16. Then Go to Analysis tab, select Analysis command and add the perform analysis command.

17. The 3D rendered view of the above bridge is illustrated below.

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Analytical Results:

Bridge has been analyzed and check for different load combination and different displacement for different scenarios has been record.

Maximum node displacements is recorded as 2 mm.

Maximum Base reactions are recorded axial force as 0 KN and moment as 1714.735KN-m.

Maximum shear force recorded in beam in Fy direction is 292.186 KN.

Maximum Bending Moment recorded in beam in Mz direction is 1714.735 KN-m.

Maximum Shear Force in SQX (local) direction for deck slab is recorded as 278.679 KN/m2.

Maximum Shear Force in SQY (local) direction for deck slab is recorded as 184.211 KN/m2.

Maximum Moment in MX (local) direction for deck slab is recorded as 90.5914 KN-m/m.

Maximum Moment in MY (local) direction for deck slab is recorded as 13.8423 KN-m/m.

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Conclusion:

Different results have been found under the temperature loads,

Maximum node displacements is recorded as 2 mm.

Maximum Base reactions are recorded axial force as 0 KN and moment as 1714.735KN-m.

Maximum shear force recorded in beam in Fy direction is 292.186 KN.

Maximum Bending Moment recorded in beam in Mz direction is 1714.735 KN-m.

Maximum Shear Force in SQX (local) direction for deck slab is recorded as 278.679 KN/m2.

Maximum Shear Force in SQY (local) direction for deck slab is recorded as 184.211 KN/m2.

Maximum Moment in MX (local) direction for deck slab is recorded as 90.5914 KN-m/m.

Maximum Moment in MY (local) direction for deck slab is recorded as 13.8423 KN-m/m.