concrete shell element

CONCRETE SHELL ELEMENTS

Session -2CONCRETE SHELL ELEMENTSUmesh RajeshirkeManaging Director SPECTRUM Techno Consultants Pvt Ltd, Navi MumbaiWORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112Mr. Umesh Rajeshirke has completed his BE Civil form VJTI (Univ. of Bombay) and M.S. from IIT, Madras. He has over 27 years of experience in planning & designing of long span bridges, precast segmental & cable stayed bridges. He has also involved in design of number Nuclear Containments, tall chimneys, Natural Draught Cooling Towers and maritime structures. Actively involved in various code committees

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE1CONCRETE SHELL ELEMENTSMethod for design of shell element is given in annexure B1 of the code.

This method is generally used when the analysis is performed using finite element method for structures like fish belly or curved box girders.

Verification at ULS is to be performed adopting the sandwich model for shell elementsForce Resultants of Shell Element.Out-of-plane moments and twisting moments are converted into stress resultants acting planes of the top and bottom layers.

The core/middle layer is designed to carry the out of plane shear force.

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE2ICI Workshop, New Delhi, 02-04 May 2013CONCRETE SHELL ELEMENTSThe method is broadly described in following three steps:

Carry out FEM analysis (generally elastic, linear) of structure with geometry assumed initially, for all applicable loads and load combinations and get the results (i.e. nEdx, nEdy, nEdxy, mEdx, mEdy, mEdxy, vEdx, vEdy, and principal stresses s1, s2, s3) at required locations.

Find out whether the element is cracked or not, using Eqn. B-1-1 of the code. If the element is un-cracked, the only verification required is to check that minimum principal stress, s3 (i.e. maximum compressive stress) does not exceed the design compressive strength, fcd.

If the element is cracked, follow the method using sandwich model to find out the required reinforcement.

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTSCheck for cracking

Where

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE4ICI Workshop, New Delhi, 02-04 May 2013 CONCRETE SHELL ELEMENTSCalculation of reinforcement using sandwich model:Steps involved in this method are given below:1. Split the shell element in three layers as shown in figure below:

The Sandwich ModelTwo outer layers resist the membrane actions arising from nEdx, nEdy, nEdxy, mEdx, mEdy, mEdxy,

Inner layer carries the shear forces vEdx, vEdy.

The thickness of the different layers should be established by means of an iterative procedure

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTS2. Design of outer layers for membrane action:

Determine the forces in outer layers of sandwich model using equation B1-13 to B1-20 of the code or by using simplified approach in section B1-13 & 14.

Basically, the membrane forces, nEdx, nEdy, nEdxy are divided between the two layers and the bending moments, mEdx, mEdy, mEdxy are converted into ( +- m/z ) forces in top and bottom layers.

These forces are depicted here in figures on next slideWORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTSAxial Forces & Bending Moments in Outer layersMembrane Shear forces and Twisting Bending Moments in the Outer Layers2. Design of outer layers for membrane action (Cont)

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTSDesign the outer layers as membrane element using method given in section 9 of the code.

If it is not possible to satisfy the design rules given in section 9, then as suggested in clause B1.15 of the code, either

increase the concrete cover and consequently reduce the internal lever arm oruse different values for lever arms, zn and zt with zn > zt ; internal concrete stresses should then be added vectorially orIncrease the layer thickness to satisfy the concrete

2. Design of outer layers for membrane action (Cont )WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTS3.Design of inner layer for out of plane shear:Out of plane shear forces vEdx and vEdy are applied to the inner layer with the laver arm zc , determined with reference to the centroid of the appropriate layers of reinforcementFor the design of the inner layer the principal shear vEdo and its direction jo should be evaluated as follows:

In the direction of principal shear the shell element behaves like a beam and the appropriate design rules should therefore be applied. In particular clause 6.2.2 of the code should be applied for members not requiring shear reinforcement and clause 6.2.3 should be applied for members requiring shear reinforcement. In expression 6.2a, r1 should be taken as

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTSWhen shear reinforcement is necessary, the longitudinal force resulting from the truss model vEdo cotq gives rise to the following membrane forces in x and y directions and shall be added to the forces obtained in outer layers:

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTSWorked Examples:

WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTS



WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE CONCRETE SHELL ELEMENTSICI Workshop, New Delhi, May 2013






, Reinforcement provided in Y-dirn is sufficient.




WORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE

CONCRETE SHELL ELEMENTS* fcd = 0.541 * 13.4 = 7.262 MPaWORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE24ICI Workshop, New Delhi, 02-04 May 2013 CONCRETE SHELL ELEMENTSThank youWORKSHOP ON CODE OF PRACTICE FOR CONCRETE ROAD BRIDGES IRC:112 2011, ORGANISED BY ING-IABSE, 11-12 JULY 2014, KOLKATA ING-IABSE25ICI Workshop, New Delhi, 02-04 May 2013

concrete shell element

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