21. Saddles - Calculation of the horizontal longitudinal reactions (RaHL) When do the sliding saddle


Ans: It depends on the friction factor input in the dialog of the saddles between the sliding saddles and the concrete or the plate under the sliding saddles.

A small friction factor value indicates that a PTFE plate or in some cases rolling bars have been installed.

The values of the longitudinal loads (RaHL) are calculated as follow:


No.

Support saddles Location (mm) Stiffness
(daN/mm)

Vertical

Horizontal

Combined

Reactions
(daN)

Shear Loads
(daN)

Bending moments
(daN∙m)

Reactions
Transverse

(daN)

Shear Loads
(daN)

Bending moments
(daN∙m)

Reactions
Longitudinal

(daN)

Reactions
(daN)

Shear Loads
(daN)

Bending moments
(daN∙m)

1

500.0

2,716.2

-324.1
2,392.2

-144.2
-2,424.7

0.0

0.0

0.0

2,402.7

2,716.2

-324.1
2,392.2

-144.2
-2,424.7

2

4,500.0

4,190.7

-1,623.1
2,567.7

-2,245.8
-697.1

0.0

0.0

0.0

-1,629.2

4,190.7

-1,623.1
2,567.7

-2,245.8
-697.1

3

8,500.0

2,057.6

-1,433.9
623.8

-1,134.0
-744.0

0.0

0.0

0.0

-521.1

2,057.6

-1,433.9
623.8

-1,134.0
-744.0

4

11,500.0

673.9

-349.8
324.1

-333.5
-144.2

0.0

0.0

0.0

-252.4

673.9

-349.8
324.1

-333.5
-144.2


The fixed saddle is located in this example on the left hand.

 How are the RaHL values calculated? Run the model with a friction factor equal to 0 and you will obtain the values of vertical reaction loads used for the calculation of RaHL (as shown here after):

No.

Support saddles Location (mm) Stiffness
(daN/mm)

Vertical

Horizontal

Combined

Reactions
(daN)

Shear Loads
(daN)

Bending moments
(daN∙m)

Reactions
Transverse

(daN)

Shear Loads
(daN)

Bending moments
(daN∙m)

Reactions
Longitudinal

(daN)

Reactions
(daN)

Shear Loads
(daN)

Bending moments
(daN∙m)

1

500.0

2,162.0

-324.1
1,837.9

-144.5

0.0

0.0

0.0

0.0

2,162.0

-324.1
1,837.9

-144.5

2

4,500.0

5,253.1

-2,177.3
3,075.8

-2,181.7

0.0

0.0

0.0

0.0

5,253.1

-2,177.3
3,075.8

-2,181.7

3

8,500.0

1,559.4

-925.8
633.7

-585.1

0.0

0.0

0.0

0.0

1,559.4

-925.8
633.7

-585.1

4

11,500.0

664.0

-339.9
324.1

-144.5

0.0

0.0

0.0

0.0

664.0

-339.9
324.1

-144.5


In this example, the mass of the each saddle is 181 kg (177.4 daN).

The friction factor is equal to 0.3

The loads on the sliding saddles are equal to:

W2ini = 5253.1 + 177.4 = 5430.5 daN                  RaHL2 = 5430.5 x 0.3 = 1629.2 daN

W3ini = 1559.4 + 177.4 = 1736.8 daN                 RaHL3 = 1736.8 x 0.3 = 521.1 daN

W4ini = 664 + 177.4 = 841.4 daN                         RaHL4 = 841.4 x 0.3 = 252.4 daN

The sign is – for these loads.

 The system is on equilibrium è S RaHL = 0

The load on the fixed saddle is equal to:  RaHL1 = 1629.2 + 521.1 + 252.4 = 2402.7 daN

When the longitudinal loads exist, the vertical loads are modified.

These modified values are due to the moments