Module 1:Unreinforced Masonry Building AssessmentWorked example end wall element

Exercise

5m

5m

5m

1m

8m

Exercise

H

t

W

W

EQ Stability load combination = 0.9D + 1.25E

And

DESIGN CAPACITY DEMAND

so

M retrofit restoring + M 0.9D restoring 1.35 x 1.25 x ME overturning

1.35 = Knowledge factor used with Italian Macro Element method

(needs better picture)

Using the Italian Macro Element method to assess end wall separation with no side wall restraint

Exercise

H

t

W

W

What acceleration, , is required to initiate overturning (without retrofit)?

Quick check of 1m vertical strip of wall

M0.9D restoring 1.35 . 1.25 . ME overturning0.9W.t/2 1.35 . 1.25 . W . H/2 0.9 . t/1.35 . 1.25 . H 0.9 . 980 / 1.35 . 1.25 . 16000 = 0.033 (g)

Using the Italian Macro Element method to assess end wall separation with no side wall restraint

CAPACITY

Exercise

H

t

W

CT W

What is the overturning Moment Demand at the design earthquake?

CT = C . Z . I . P . KpCT = 0.08 . 1.0 . 1.5 . 1.0 . 4

(P = 1 for part on ground)

CT = 0.48 (g)(assuming there is no resonance of the part. NBC 105 Clause 12.5.2See check on next slide)

CAPACITY / DEMAND = 0.033/0.48 = 0.07

7% Nepal Building Code. Therefore topples with code earthquake

Using the Italian Macro Element method to assess end wall separation

DEMAND

Exercise

H

t

W

CT W

Check for resonance [NBC 105 Clause 12.5.2]

If 0.6 < T1 building /Tpart < 1.4 then Kp 2xKpFor vertical spanning rocking cantilever[Eqn 10.24 NZSEE Guideline section 10 URM]

Tp = sqrt(0.65 . h [1+(t/h)2]) Tp = 3.4s

T1 building 0.09H/Sqrt(D) [NBC 105 Cl 12.5.2]T1 building 0.09 . 16 / Sqrt(~30m to 60m) 0.26s to 0.18sTherefore T1 building /Tpart 0.01 to 0.05so resonance will not occur, no need to double Kp

Using the Italian Macro Element method to assess end wall separation

DEMAND

Exercise

H

t

W

CT W

What is the overturning Moment Demand at the design earthquake?

Unit weight = 18kN/m3

W = 18 . 16 . 0.98 = 282kN/mCT = 0.48 H = 16 mt = 0.98m

M1.25E overturning = 1.35 . 1.25W CTH/2 = 1827 kNm/m

M 0.9D restoring = 0.9Wt/2 = 129 kNm/m

Using the Italian Macro Element method to assess end wall separation

RETROFIT OPTION

FP

Required M retrofit restoring 1827 129 = 1700 kNm/m

Exercise

H

t

W

CT W

What tie force is required at the head of the wall?

M retrofit restoring = Fp . H1700 = FP . 15m

FP = 113 kN / m REQUIRED

Say wall length = 7m. Gives 791kN total

Two ties at head = 396 kN/ tie

Using the Italian Macro Element method to assess end wall separation

RETROFIT OPTION

FP

Exercise

H

t

W

CT W

What size tie rod required for 396 kN?

Consider Reidbar allthread reinforcing rod at 500 MPa yeild strength

Try 24 mm rod

T = Asfy = 0.9 . 452 mm . 500 MPaT = 203 kN

So 2 x RB24 rods required each side at top of wall. Quite a large force to transfer

Using the Italian Macro Element method to assess end wall separation

RETROFIT OPTION

FP

ExerciseQuestions?

Tension ties at all three/four floors?

All equal or different forces at each floor?

Tie into diaphragm or in-plane walls?

Other end wall separation failure modes?Other out of plane modes?

Will wall rotate about bottom of foundation or about seating on plinth?

Effect of considering ground bearing capacity or masonry compressive strength on overturning resistance? (will reduce capacity further)

RefinementsRefine assumptionsSeek drawings, site measure, ground information

Refine Exercise

3.7m

3.1m

2.6m

2.4m

6.6m

Refined assumptions after investigations

1m

3m

2m

2m

2m

2m

0.6m

14.4m to apex

Refine Exercise

3.7m

3.1m

2.6m

2.4m

6.6m

Find wall weight, W

1m

3m

2m

2m

2m

2m

0.6m

Area = 12.4m . 6.6m ground to eave+ 2.0m . 6.6m / 2 gable- 1m (3+2+2+2)m openings

W = 66.2m2 . 18kN/m3 = 1200 kN

Refine Exercise

H

t

W

x W

Consider effect of actual strength of underlying material (brick or soil) on over turning capacity.

Lets say that after inspection of building we have assessed that;

- Foundation thickness is same as wall thickness

- Wall is most likely to rotate about bottom of foundation

- Bearing capacity of soil under foundation is 300 kPa

Using the Italian Macro Element method to assess end wall separation with no side wall restraint

CAPACITY

300 kPa

Refine Exercise

H

t

W

x W

So we will find width of bearing resistance on bottom of rocking element using qu = 300 kPa soil capacity

Rectangular stress block assumed

Stress block width b = W / qu / wall lengthb = 1200kN / 300 kPa / 6.6mb = 600m

Find eccentricity et = 980mme = (t b)/2e = 190mm

Using the Italian Macro Element method to assess end wall separation with no side wall restraint

CAPACITY

300 kPa

b

CL

e

Refine Exercise

Now what acceleration is required to initiate overturning?

0.9MD restoring 1.35 . 1.25 . ME overturning0.9W.e 1.35 . 1.25 W . h = 0.9 . e/1.35 . 1.25. h = 190mm / ~6000mm = 0.017 (g)Compare with previous value 0.033 (g)Refined capacity assessment is half the initial value

Similar effect if rocking on masonry or concrete, but less extremeIf checking rotation about plinth level then would use fm value instead of soil qu

Using the Italian Macro Element method to assess end wall separation with no side wall restraint

CAPACITY

H

t

W

W

300 kPa

b

CL

e

Refine Exercise

What is the overturning Moment Demand at the design earthquake?

CT = C . Z . I . P . KpCT = 0.08 . 1.0 . 1.5 . 1 . 4

(P = 1 for part on ground but for parts supported by structure above ground P = 1 + h/H )

CT = ~0.48 (g) same as before(as before, no resonance of the part)

CAPACITY / DEMAND = 0.017/0.48 = 0.04

Only 4% Nepal Building Code.

Using the Italian Macro Element method to assess end wall separationwith no side wall restraintDEMAND

H

t

W

CT W

CL

e

b

Refine Exercise

W

CT W

What is the overturning Moment Demand at the design earthquake?

Try ties at each levelW = 1200kN CT = 0.48h overturning = ~6 m e = 0.19 m

ME overturning = 1.35 . 1.25 .W .CT . hME overturning = 5832 kNm

0.9M D restoring = 0.9W.e = 205 kNm/m

Will try 4 equal anchors distributed up the building using virtual work calculation

Using the Italian Macro Element method to assess end wall separation

RETROFIT OPTION

FP

FP

FP

FP

13.4m

9.9 m

7.3m

4.2mh

Required M retrofit restoring 5832 205 = 5627kNm/m

CL

e

b

Refine Exercise

What tie force is required at the head of the wall? Lets choose four equal strength anchors

M retrofit restoring = (Fp . h restoring )5627= FP (13.4+9.9+7.3+4.2)

FP = 162 kN REQUIRED

Four levels of ties. Gives 648kN total (Total is 80% of top only tie option total)

Two ties each level = 81 kN/ tie

Using the Italian Macro Element method to assess end wall separation

RETROFIT OPTION

W

CT W

FP

FP

FP

FP

13.4m

9.9 m

7.3m

4.2m

Refine Exercise

W

CT W

What size tie rod required for 81 kN?

Consider Reidbar allthread reinforcing rod at 500 MPa yeild strength

Try 16 mm rod

T = Asfy = 0.9 . 201 mm . 500 MPaT = 90 kN

So one RB16 rod required each side at each level

BUT need to consider maximum force from all potential failure modes at each location before finalising decision

Using the Italian Macro Element method to assess end wall separation

RETROFIT OPTION

W

FP

FP

FP

FP

13.4m

9.9 m

7.3m

4.2m

Refine Exercise - Further Work

Regardless of retrofit option chosen, need to consider all possible modes of failureDesign tie for max(FP FP2 FP3 FP4)

Using the Italian Macro Element method to assess end wall separation

RETROFIT OPTION

W

CT W

FP

FP

FP

FPW2

CT W2

FP2

FP2

FP2W3

CT W3

FP3

FP3

W4

CT W4FP4

Also consider other modesOut of plane buckling?

P = 1

P = 1+h/H

P = 1+h/H

P = 1+h/H

Refine Exercise

Level s1 s2 s3 s4 Maximum4 81 kN ? ? ? ?

3 81 kN ? ? - ?

2 81 kN ? - - ?

1 81 kN - - - 81 kN

Using the Italian Macro Element method to assess end wall separation

RETROFIT OPTION

Tabulate force required for each scenario

And also consider other modes such as out of plane buckling