3. MODELO DE CLASIFICACIÓN DE LOS ESTILOS DE ENSEÑANZA (EDE) 1. Referentes para la construcción de un modelo de EdE
3.2. Modelo y cuestionario sobre EdE desde un enfoque cognitivo- cognitivo-constructivista
C.2.1 Design criteria. Consider the design for a pipe having an internal diameter of 1 000 mm and for an internal pressure of 5 bar (0.5 N/mm2).
The pipe is assumed to be manufactured by hand lay-up for any chopped strand mat and woven roving constructions, (k1 = 1.5), and machine controlled for continuous rovings construction, (k1= 1.5).
In addition the following assumptions will be made:
a) the long term behaviour, k2 = 1.2;
b) the cyclic stressing 104 for the life of the pipe, k4 = 1.4;
c) full post cure will be used, k5 = 1.1.
For the purpose of the illustration two operating temperatures will be considered with resins being required with different heat distortion temperatures.
The circumferential unit load calculated from equation (7) = 250 N/mm.
Therefore the laminate shall be designed so that its design strength is not less than this calculated value [see equation (6)].
For the purposes of these examples it is assumed that the axial load, Qa, does not exceed Qc so that a laminate designed to withstand the latter will be satisfactory.
C.2.2 Design constructions
C.2.2.1 All chopped strand mat (CSM) construction. For this construction the operating temperature is assumed as 60 °C, the heat distortion temperature of the resin to be used is 100 °C and its fracture strain is 3.5 %.
a) Determine the design factor K [see equation (1)].
K = 3 × k1 × k2 × k3 × k4 × k5
= 3 × 1.5 × 1.2 × 1.0 × 1.4 × 1.1
= 8.3
b) Determine the allowable design strain.
Allowable resin strain (see 14.4.2.3) º = 0.1ºR
= 0.1 × 3.5
= 0.35 %
As this is greater than 0.2 % this latter value is taken as the allowable resin strain.
Allowable laminate strain [see equation (2)].
= 0.17 % ex u
XxK
---=
200 100×
14000 8.3×
---=
The allowable design strain, ºd, is taken as the least of these = 0.17 % c) Determine the laminate construction.
Overall unit modulus [see equation (4)].
XLAM = Xmn
= 14 000 mn
Laminate design unit loading [see equation (5)].
The design requirement is satisfied if ULAM is at least equal to the circumferential unit load [see equation (6)].
hence 0.17 × 140 × m × n = 250 m × n = 10.5 kg/m2 glass
Thus a suitable construction of laminate would be as follows [see Figure 16(a)]:
C.2.2.2 Chopped strand mat and woven roving construction. In practice a large proportion of laminates are not all CSM and they incorporate woven rovings. A simple form of this type of construction is shown in Figure 16(b) where alternate layers of woven roving complying with the requirements of
BS 3749 (800 g/m2 ) and CSM (450 g/m2 ) are used.
For the calculation an operating temperature of 80 °C is assumed and a dual resin system will be used with the following properties.
The method of calculation is as follows.
a) Determine the design factor K [see equation (1)].
K = 3 × k1 × k2 × k3 × k4 × k5
= 3 × 1.5 × 1.2 × 1.25 × 1.4 × 1.1
= 10.4
b) Determine the allowable design strain.
Allowable resin strain (see 14.4.2.3).
Resin A = 0.1 × 2.5 = 0.25 % Resin B = 0.1 × 1.75 = 0.175 %
As the value for resin B is less than 0.2 % its value (i.e. 0.175 %) is the allowable resin strain.
ULAM = ºdXLAM
resin rich inner layer with tissue —
two layers of 300 g/m2 (one at each surface) 0.6 kg/m2 sixteen layers of 600 g/m2 9.6 kg/m2
one layer 450 g/m2 0.45 kg/m2
resin rich outer layer with tissue —
10.65 kg/m2
Property Resin
A B
Fracture strain 2.5 % 1.75 %
Heat distortion temperature 125 °C 100 °C 0.17
--- 14000 m100 × × ×n
=
Licensed copy: Mr. National University Singapore, National University of Singapore, Version correct as of 19/11/2012 08:31, (c) The British Standards Institution 2012
Allowable laminate strain [see equation (2)].
Chopped strand mat (CSM):
Woven rovings (WR):
The allowable design strain, ºd, is taken as the least of these = 0.137 %.
c) Determine the laminate construction.
The resin A is selected to form an inner corrosion resistant laminate (2 × 600 g/m2 ) and as the resin for the resin rich inner and outer layers with tissue.
If the number of layers of woven rovings is n, the number of CSM (450 g/m2) is n – 1. These are in addition to the corrosion resistant laminate and the usual CSM (300 g/m2) laminate under the outer resin rich layer.
Laminate design unit loading (in N/mm) [see equation (5)].
As this value shall be at least equal to, Qc, i.e. 250 N/mm n = 9.01 say 10.
Thus a suitable construction of laminate would be as follows [see Figure 16b)].
C.2.2.3 Chopped strand mat and continuous rovings construction. In this construction the continuous roving laminates are laid by a machine controlled process between a CSM (2 × 600 g/m2) corrosion resistant laminate and a CSM (450 g/m2) under the outer resin rich layer [Figure 16c)]. One type of resin as in C.2.2.1 is considered.
a) Determine the design factor [see equation (1)].
Chopped strand mat (CSM):
K = 3 × k1 × k2 × k3 × k4 × k5
= 3 × 1.5 × 1.2 × 1.0 × 1.4 × 1.1 = 8.3 Continuous rovings (CR):
K = 3 × 1.5 × 1.2 × 1.0 × 1.4 × 1.1 = 8.3
(2 × 0.6 × 14000 + 0.45 × 14000 ×
× (n– 1) + 0.8 × 16000 × n)
Resin A resin rich inner layer with tissue two layers of 600 g/m2 CSM —
0.6 kg/m2
Resin B
ten layers of 800 g/m2 WR alternate with nine layers 450 g/m2 CSM
one layer 300 g/m2 CSM
8.0 kg/m2 4.1 kg/m2 0.3 kg/m2 Resin A resin rich outer layer with tissue —
13.0 kg/m2
&CSM UCSM XCSMK
--- 200 100× 14000 10.4×
--- 0.137 %
= = =
eWR UWR XWRK
--- 250 100× 16000 10.4×
--- 0.141 %
= = =
ULAM = edXLAM 0.137 --- 100
=
b) Determine the allowable design strain.
Allowable resin strain (see 14.4.2.3) º = 0.1 ºR
= 0.1 × 3.5 = 0.35 %
As this is greater than 0.2 % this latter value is taken as the allowable resin strain.
Allowable laminate strain [see equation (2)]
The allowable design strain, ºd, is taken as the least of these = 0.17 %.
c) Determine the laminate construction.
Assume the continuous rovings are laid at an angle of 55° to the pipe axis with a mass per layer of 600 g/m2 and n laminates are used.
Circumferential unit modulus of the laminate construction [see equation(4)].
XLAM(c) = 14000 × (2 × 0.6 + 0.45) + 9900 × 0.6 × n
The design requirement is satisfied if XLAM(c) is at least equal to the circumferential unit load [see equation (6)].
Hence (14000 × (2 × 0.6 + 0.45) + + 9900 × 0.54) × 0.6 × n) = 250 n = 41.73 say 42
Thus a suitable construction of laminate would be as follows:
Because this pipe does not have similar properties in circumferential and axial directions, the allowable loading in the axial direction should now be checked.
Provided the axial load does not exceed 136 N/mm, the above laminate will be satisfactory. If this is not the case then the allowable axial loading will have to be increased to the design value by further application of additional layers of chopped strand mat, woven rovings or continuous rovings.
CSM:
CR:
4) Factor relating to angle of lay (see Table 3).
resin rich inner layer with tissue —
two layers of CSM (600 g/m2) 1.2 kg/m2 42 layers CR (600 g/m2) laid at 55° 25.2 kg/m2 one layer of CSM (450 g/m2) 0.45 kg/m2 resin rich outer layer with tissue —
26.85 kg/m2
ULAM(a) = (14000 × (1.2 + 0.45) + + 4500 × 0.54) × 0.6 × 42)
= 136 N/mm.
&x u XxK
---=
200 100× 14000 8.3×
---= 0.17 %
=
&x u X xK
---=
550 100× 28000 8.3×
---= 0.24 %
=
0.17 --- 100
0.17 --- 100
Licensed copy: Mr. National University Singapore, National University of Singapore, Version correct as of 19/11/2012 08:31, (c) The British Standards Institution 2012
If circumferential and axial loads are applied simultaneously it is necessary to establish whether the allowable loads under these conditions are less than those in the above calculation.
This may be done by the construction of a biaxial failure envelope (see Figure 17) using information obtained from the physical testing of the proposed laminate.
The following conditions are applied:
Where Ua and Uc are the allowable axial and circumferential unit loads under biaxial loading.
The completed biaxial failure envelope shows the combinations of loads which may be applied to the laminate, for example, from Figure 17, a combined load of Ua = 80 N/mm and Uc = 160 N/mm would be satisfactory but a combination of Ua = – 80 N/mm and Uc = 160 N/mm would not be satisfactory.
C.2.3 Thickness calculations. If we assume a glass content of 30 % for CSM, 50 % for woven rovings and 65 % for continuous rovings Figure 2 gives the thicknesses expected for these constructions for a resin density of 1.3 as follows:
Therefore the thicknesses of the laminates (excluding surface reinforced gel coats) in the three constructions are as follows.
a) The all CSM construction of example C.2.2.1 requires a total mass of 11.25 kg/m2 glass and the design thickness of this laminate is calculated as:
2.2 × 10.65 = 23.4 mm
b) The mixed CSM/WR construction of example C.2.2.2 will have a design thickness:
c) The mixed CSM/CR construction of example C.2.2.3 will have a design thickness: