14 04 24 CJOR Worked Example Rev A

8/16/2019 14 04 24 CJOR Worked Example Rev A

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S t r u c t u r a l U s e o f G l a s s i n B u i l d i n g s S e c o n d E d i t i o n )

B y C h r i s O’ R e g a n B E n g H o n s ) C En g M I S t r u c t E

Pa ge | 1

W o r k e d e x a m p l e f o r f l o o r p l a t e d e s i g n

A glass floor plate is to be installed that sits over a basement. The support is via a steel frame with a 1 .5m x 1.5m g rillage ofbeam s. This frame provides a continuous supp ort and the f ollowing analysis and design of t he glass floor plate p rovisionall yassumes it to be infinite ly stiff. The following calculation d etermine s the thickness of the glass required for the floor plate.

The below floor loadings are typical for domestic use and should be used for design:

Characteristic variable a ction q k = 1 .5 k N / m 2

Characteristic point action Qk= 3.0kN

The glass will not be sandbla sted and wi ll be ename lled on the wearing side. This will not im pact on t he design of the glassas the enamelling is on the comp ression side of the floor plate .

The glass is to be m ade up of three layers of glass lamina ted with PVB, It is assumed t hat the top sheet will be toughenedand not included in the stress calculations although will be considered for deflection. To provide the most effective postbreakage behaviour the lower two sheets will be heat strengthened .

Two action duratio ns apply: permanent and short.

Permanent act ion condit ion

Determine d esign strength of glass using Append ix C.

f g;d = kmodkspf g;k

M:A

+ kv(f b;k - f g;k)

M:v

For load du ration > 5 0 years, k m od = 0.29

k mo d = 0 .29 , k sp = 1 .0 ,f g;k = 4 5 N/ m m2 f b;k = 7 0N / m m 2 , k v = 1.0, M: A = 1.6 and M: v = 1.2.

f g;d = 0.29 × 1.0 × 45N/mm1.6

+ 1.0(70N/mm - 45N/mm)

1.2 = 29N/mm2

Variable actio n condition i.e. short duration load

For load durati on of 5 hours, for pedestrian action; k m od = 0.60

f g;d =

0.60 × 1.0 × 45N/mm1.6

+1.0(70N/mm - 45N/mm)

1.2

=

37.7N/mm2

Determine t he effective thickness of the glass required b ased on design strength





Pa ge | 2

Try two 1 2m m t hick pl ies and one 1 2m m t hick sacri f ic ial ply. The laminate is a PVB based material and is 0 .76m m thick.

In order to calculate the effective thickness of the glass pane, the shear interaction between the plie s of the laminated g lassvia the PVB interlayer must be accounted for.

The simp lified m ethod of d eterminin g stress of glass within each ply is as follows.

The effective thickness of the glass when considering deflection d ue to bend ing is:

hef;w= hk 3 + 12 hkhm,k

2

i

k

3

where:h k is the thickness of each plyh m, k is the distance between the mi ddle of the p ly to the centre of the laminat ed glass pane.

When calculating stress the equivalent thickness is calculated f rom:

;; ; +2;

where:h j is the thickness of each plyh m, j is the distance between the mi ddle of the p ly to the centre of the laminat ed glass pane.

Assuming a value of 0.1 for when considering variable actions and ‘0’ w hen assessing effects due to permanen t actions,two effective thicknesses need to be calculated.

Effective thickness in permanent action condit ion

The effective thickness of the lam inated g lass with respect to permanent act ion is as follows:

hef;w = 123mm + 12

3mm 3

= 15.1mm

Note that the variable equates to ‘0’ hence it is not include d in the calculati on. Addition ally the toughened glass top ply isnot included w hen determinin g the overall depth of the glass as it is considered to be sacrificial.

Effective thickn ess in Variable Action Condition

The effective thickness of the lam inated g lass with respect to variable actio n is as follows:

hef;w = 12

3mm +

12

3mm

+

12

×

0.1

×

(12mm×

6.42mm + 12mm × 6.4

2mm)

3

= 16.7mm

This is the effective thickness of the lami nated gla ss that is to be used for deflectio n calculation s.

The effective thickness of the laminat ed glass for ben ding stress is as follows:

;; 16.7mm

12mm+2×0.1×6.4mm=18.7mm

Note how the thickness has increased from 1 5.1m m to 16 .7mm due to the inclusion of shear interact ion within the PVB

based interlayer, which is then increased to 18 .7m m when calculati ng stress





Pa ge | 3

Bendi ng stress check

There are two action condit ions to check for: perm anent and variable (short). With respect to th e perman ent conditio n, thefol lowing appl ies:

Permanent Actions due to self-weight = 0.03 6m x 25 kN/ m 3 = 0 .9 k N/ m 2

(N o t e this includes the 12m m thick toughened glass top ply which is not included when determining the effect ive thicknessof the gla ss.)

Partial factor for perma nent action q=1.35

UD L ult = 0 .9 k N / m 2 x g = 0 . 9k N/ m 2 x 1 . 3 5 = 1 . 2 2 k N/ m 2

The app lied bendi ng stress to the plate during the perm anent conditio n is defined in Table 11 .4 of Roark’s Formulas forStress and Strain – 8 th Edit ion as:

max = qb2

; , = 0.287

The variable is dependen t upon the ratio of geom etry of the plate. In this instance the ratio of the dime nsions of the plateis 1; therefore = 0 .287

max = 0.287 × 1.22kN/m × 1.52m

0.01872m

= 2.3×10kN/m2 =2.3N/mm

2 .3 N/ m m 2 < 2 9N / m m 2 OK

The app lied bendi ng stress to the plate during the variable action condit ion is:

1 . 2 2 kN / m 2 + 1 . 5 kN / m 2 x q = 1 .2 2 k N / m 2 + 1 .5 k N/ m 2 x 1 .5 = 3 .47kN/ m 2

There are two effects to consider for the variable action co nditio n: that of the UDL and the point load .

UD L

max = 0.287 × 3.47kN/m × 1.52m

0.01872m = 6.4×10kN/m2 =6.4N/mm

6 .4 N/ m m 2 < 3 7 .7 N / m m 2 OK

Concentrated point action

The area over which the act ion is appl ied is 50 mm x 50mm = 25 00 mm 2

equivalent circle area radius r o =r if r 0.5t = 2 5 0 0 mm

= 28 .2mm

Bending stress at point of concentrated loa d:

= 3 ;; (1+) ln 2

Where:

W is the design concentrated po int action

is Poisson’s Ratio





Pa ge | 4

is a variable that i s dependent u pon the ratio of geome try of the plate. See Table 1 1.4 of Roark’s Formulas for Stress andStrain – 8 th Editi on.

In this instance the ratio of the dime nsions of the plate equate t o 1, therefore =0.435

Partial factor for variable concentrat ed action Q=1.5

point load = 3 × 3000 × 1.5

2 ×× 18.72 (1 + 0.22) ln2 × 1500mm

× 28mm + 0.435 = 29.1N/mm2

including self-weight oa =29.1N/mm2 + 2.3N/mm

2=31.4 N/mm

2

3 1 .4 N / m m 2 < 3 7 .7 N / m m 2 OK

Deflect ion check

It Is safe to assume all three panels of glass participate in restricting defl ectionEquivalent thick ness of 3 layers is as follows:

hef;w = 123mm + 12

3mm + 12mm 12 × 0.1 × (12mm ×

12.82mm + 12mm × 0mm 12mm× 12.8mm)

3

=21.5mm

Equivalent I value = ×. = 1.24×10mm

Taking th e point load as the worst case condition:

Serviceabilit y state de flection =

3000N×1500

mm

48×70000N/mm ×1.24×10mm = 2.4mm

Assuming a span/ depth rat io of 250 , the maximum al lowable deflect ion is 6m m > 2 .4mm therefore the f loor plate passesboth serviceability and strength checks.

Post-failure check

As all three sheets of glass could fail the only truly reliab le test for the propo sed design is to undergo physical testin g of thedesign to confirm its suitabilit y.

Some schools of thought suggest a design method where one sheet is assumed to remain intact. This can offer somemeasure of com fort but d oes not cover the case where all three sheets are broken. This approach is il lustrated below.

Two action duratio ns apply: permanent and short.

Permanent act ion condit ion

The strength of the glass is the same for the intact f loor plate.

Bendi ng stress check

In the post-failure conditi on there remain the two action cond itions to check f or: permanent and variable (short). Withrespect to the permane nt condition, the following applie s:

Actions are similar to intact condit ion i .e. 0.9 k N/ m 2

Partial factor for perma nent action g=1.0 due to accidental condit ion





Pa ge | 5

UD L ult = 0 .9 k N / m 2 x g = 0 .9 k N / m 2 x 1 . 0 0 = 0 . 9 k N / m 2

When taking into account t he two way spanning action of the floor plate, the app lied bend ing stress to the plate d uring thepermanent condit ion is:

max = qb

2

hef:w2 , = 0.287

max = 0.287 × 0.9kN/m × 1.52m

0.0122m

= 4.0×10kN/m2 =4.0N/mm

4 .0 N/ m m 2 < 2 9 .0 N / m m 2 OK

The app lied bendi ng stress to the plate during the variable action, short duration cond ition is:

Partial factor for varible action q=1.0 due to accidental condit ion

UD L ult = 0 .9 k N / m 2 + 1 .5 k N / m 2 x q = 0 .9 k N / m 2 + 1 .5 k N/ m 2 x 1 .0 = 2 .4kN/ m 2

There are two effects to consider for the variable action co nditio n: that of the UDL and point load .

UD L

max = 0.287 × 2.4kN/m × 1.52m

0.0122m

= 10.8×10kN/m2 =10.8N/mm


2=13.1 N/mm

2

1 3 .1 N / m m 2 < 3 7 .7 N / m m 2 OK

Point load check

Although this is an accidental condit ion, the point l oad check st i l l appl ies.

Partial factor for variable concentrat ed action Q=1.0

concentrated action = 3 × 3000 × 1.0

2××122mm

(1 + 0.22) ln2 × 1500mm

× 28.2mm+ 0.435 = 47.1N/mm2


2=49.4 N/mm

2

4 9 .4 N / m m 2 > 3 7 .7 N / m m 2 fai ls

I f the two bottom sheets remain as 14 mm and the top sheet is dropped to 8 mm then the overal l thickness wi l l remain thesame and the stress calculated above wi ll reduce to 36 .9N/ mm 2 , which is within the all owable de sign bending stress.

No deflection check requi red as it is a post-failure condit ion.

The overall thickness of the glass is 37.5 mm , which correlates closely to the span/ dept h ratio of 40.

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14 04 24 CJOR Worked Example Rev A