RF-CONCRETE Surfaces – Online Manual Version 5

Online manuals, introductory examples, tutorials, and other documentation.

RF-CONCRETE Surfaces – Online Manual Version 5

Switch to Fullscreen Mode Exit Fullscreen Mode

2.7.10.6 Shrinkage influence

Shrinkage influence

The influence of shrinkage is directly introduced in the calculation with the defined value of the free shrinkage εsh. Thus, the influence of structural restraints or redistributions of the shrinkage forces is not taken into account.

In our example, the shrinkage strain is applied with the following value:

εsh = -0.5 · 10-3 

The free shrinkage strain causes additional forces in the cross-section:

nsh,ϕ1 = -Es · εsh · as1,ϕ1+ as2,ϕ1 = -200 · 109 · -0.5 + 10-3 · 1000 + 15 · 10-6 =            = 101.5 kN/m 

The forces act for both crack states c (cracked and uncracked) with the eccentricity to the centroid of the ideal cross-section:

esh,c,ϕ1 = as1,ϕ1 · d1,ϕ1 + as2,ϕ1 · d2,ϕ1as1,ϕ1 + as2,ϕ1 - zc,ϕ1 

  • uncracked state:

esh,c,ϕ1 = 1000 · 150 + 15 ·501000 + 15 - 101.4 = 47.1 mm 

  • cracked state:

esh,c,ϕ1 = 1000 · 150 + 15 ·501000 + 15 -58.5 = 90.0 mm 

The bending moment caused by the axial force nsh,φ1 for both states c is:

msh,c,ϕ1 = nsh,ϕ1 · esh,c,ϕ1 

  • uncracked state:

msh,l,ϕ1 = 101.5 · 103 · 0.047 = 4.8 kNm/m 

  • cracked state:

msh,lI,ϕ1 = 101.5 · 103 · 0.090 = 9.1 kNm/m 

When determining the coefficient ksh,c,d for both states c, we have to distinguish:

  • for mφ1 ≠ 0:

ksh,c,ϕ1 = msh,c,ϕ1 + mϕ1 - nϕ1 · ec,ϕ1mϕ1 - nϕ1· ec,ϕ1 

  • for mφ1 = 0:

ksh,c,ϕ1 = 1         mit ksh,c,ϕ1  {1,100} 

In this example: mφ1 ≠ 0

  • uncracked state:

ksh,l,ϕ1 = 4.771 · 103 + 30 · 103 - -100 · 103 · 1.4 · 10330 · 103 -  -100 · 103 · 1.4 · 103 = 1.159 

  • cracked state:

ksh,Il,ϕ1 = 9.135 · 103 + 30 · 103 - -100 · 103 · -41.5 · 10330 · 103 - -100 · 103 · -41.5 · 103 = 1.354 

Figure 2.122 Shrinkage influence