Report from "Design of masonry"

From: Subject: Report from "Design of masonry" Date: Sat, 29 Nov 2008 16:00:32 +0100 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_000B_01C9523B.9B7DC9B0" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.5579 This is a multi-part message in MIME format. ------=_NextPart_000_000B_01C9523B.9B7DC9B0 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: http://ec6design.com/en/module/lbev?komponentId=14729&report=Report&Vaegtype=0&Hojde=2.800&ALengde=6.000&ATykk=100&VLengde=0.000&VTykk=0&HLengde=0.000&HTykk=0&FormurTykk=108&fcg=3.50&ftg=1.20&densitet=650&Ecg=1600&E0k=2200&LLast=50.0&e0=17&ExcReak=1&e5=5&TLast=0.50 =EF=BB=BF Report from "Design of masonry"

DTI xfg 1234 xr	Initials: ksa Date: 11/29/2008 Time: 3:56 PM
Project: Town Hall Component: Concrete#1	Number: 1243-26 Module: Vertical loaded storey high walls of = light=20 weight concrete

Input

Type of wall
The wall is a single-leaf wall or an inner = leaf=20 combined with a veneer wall.

Dimensions
	Height=3D 2.800 m
	Wall:	Length	Thickness
	Load carrying (actual wall)	6.000 m	100 mm
	Left supporting	0.000 m	0 mm
	Right supporting	0.000 m	0 mm

Parameters:
	Compressive strengh f_cg =3D 3.50 = MPa	Flexural strength f_tg =3D 1.20 = MPa	Density =3D 650 kg/m=C2=B3
	E-module E_cg =3D 1600 MPa
	Consequence class=3D Normal	Control class=3D Normal

Design loads
	Vertical load (positive downwards) = n_d =3D=20 50.0 kN/m	Topeccentricity (positive opposite horizontal = load)=20 e₀ =3D 17 mm
	Eccentric reaction at the footing is accepted.
	Out-of plane eccentricity e₅ =3D 5 mm	Horizontal load (wind) w_d =3D 0.50=20 kN/m=C2=B2

General pressumptions

Vertical loaded storey high walls of light weight concrete

This module "Vertical loaded storey high walls of light weight = concrete" is=20 determining the load capacity for walls without openings. For a load = bearing=20 wall with large openings it will be necessary to determine the load = capacity=20 between openings individually. A load bearing wall with small openings = can be=20 considered as an integrated wall though. In both coincidences shall the = total=20 vertical load be distributed over the effective length of the wall (i.e. = the sum=20 of the wall sections between openings). No vertical load can be = transferred=20 through an opening (naturally).

Since the load is a combination of vertical load, horizontal load and = moments=20 of eccentricity, the load capacity is not a given value, but a = mn-diagrams. The=20 given load-combination should be "inside" the mn-diagrams giving a = sufficient=20 load capacity.

A mn-diagram for a column gives the relation between a vertical load = and a=20 corresponding moment. For a column designed by a material without = flexural=20 strength there can not exist a moment without a corresponding vertical = load to=20 stabilize the column.

The load-capacity is calculated in 2 states (the un-cracked and the = cracked=20 phase).

In the un-cracked phase the flexural strength is taking into = consideration.=20 The mn-diagram is developed from the extended Navier formula taking the = column=20 effect into consideration.

In the cracked phase the flexural strength is assumed to be zero. The = mn-diagram is constructed from the Ritter formula. The load (actual = value for m=20 and n) should be "inside" only one of the curves (mn-diagram).

The actual combination of vertical load and moment is determined = from:

The vertical load on the top of the wall=20
The dead load in the upper part of the wall=20
Eccentricity in top and bottom e_e=20
Out of plane deviation of the wall=20
Horizontal load

The program determines combinations of vertical load and moment in = different=20 cross-sections and selects the cross-section with the largest moment as = the=20 design value. The combination of vertical load and moment is then = compared with=20 the mn-diagrams.

Calculations

The walls supporting = conditions
	The wall is only supported at top and=20 bottom.

Effectivce length:

The reduced column height l_s =3D = 1.00 =C3=97=20 2800 =3D 2800 mm

The slenderness ratio:
	Equivalent column thickness: t_s = =3D 100=20 mm
	l_s / t_s =3D = 2800 / 100 =3D=20 28.0 < 30 =3D> The slenderness ratio is=20 OK

Parameters:	Charac. value	Safety factor	Design value
	Compressive strength	f_cg =3D 3.50 MPa	1.60	f_cd =3D 2.19 MPa
	Flexural strength	f_tg =3D 1.20 MPa	1.70	f_td =3D 0.71 = MPa

Loads and section forces (design = values)
	Moment at the top	Vertical load =C3=97 Topeccentr. = =3D	m_top =3D	0.85	kNm/m
	Dead load of the wall		g =3D	1.79	kN/m
	Reaction at the footing	Vertical load + dead load =3D	R_fod =3D	51.79	kN/m
	Eccentricity at the footing (positive opposite = horizontal=20 load)	e_fod =3D	-17	mm

(Eccentricity is minimum(as restrained at bottom,=20 A-thickness/6)

Section forces related to = Navier-load=20 capacity
	(Critical cross-section is where at maximum moment = (in the=20 full length)).
	Resulting eccentricity in the critical = cross-section	e_Res =3D	20	mm
	Vertical force in the critical cross-section	n_Res =3D	50.40	kN/m
	Moment in the critical cross-section	n_Res =C3=97 = e_Res =3D=20 m_Res =3D	0.98	kNm/m

Section forces related to=20 Ritter-capacity
	(The critical cross-section is pressumed in middle = third, at=20 the maximum moment).
	Resulting eccentricity in the critical = cross-section	e_Res =3D	19	mm
	Normal force in the critical cross-section	n_Res =3D	50.60	kN/m
	Moment in the critical cross-section	n_Res =C3=97 = e_Res =3D=20 m_Res =3D	0.94	kNm/m

Diagram for design load capacities

Navier-capacity:
	Critical normal force:	n_cr =3D N_cr / = b_e=20 =3D	60.8	kN/m
	Factor of second order effect:	mff =3D	n_cr /	(n_cr-n)
	Criteria 1: tension stress < tension strength:	mff=C3=97=CF=83_M - =CF=83_N = <	f_td
	Criteria 2: compression stress < compression strength: =	mff=C3=97=CF=83_M + =CF=83_N = <	f_cd


Normal-	Corresponding failure moment m=20 after
force n	criteria 1	criteria 2	minimum
kN/m	kNm/m	kNm/m	kNm/m

0.0		1.176		3.646	1.176
2.4		1.168		3.461	1.168
4.9		1.157		3.280	1.157
7.3		1.142		3.101	1.142
9.7		1.124		2.926	1.124
12.2		1.103		2.755	1.103
14.6		1.079		2.586	1.079
17.0		1.051		2.421	1.051
19.5		1.020		2.259	1.020
21.9		0.986		2.100	0.986
24.3		0.949		1.944	0.949
26.7		0.908		1.792	0.908
29.2		0.865		1.643	0.865
31.6		0.818		1.497	0.818
34.0		0.767		1.355	0.767
36.5		0.714		1.215	0.714
38.9		0.657		1.079	0.657
41.3		0.597		0.946	0.597
43.8		0.534		0.817	0.534
46.2		0.467		0.690	0.467
48.6		0.397		0.567	0.397
51.1		0.324		0.447	0.324
53.5		0.248		0.331	0.248
55.9		0.169		0.217	0.169
58.4		0.086		0.107	0.086
60.8		0.000		0.000	0.000

Ritter-capacity:

	e_t	t_d - = 2e_t	k_s	n	m
	mm	mm		kN/m	kNm/m

	50		0		0.00	0.0	0.000
	42		17		0.02	0.6	0.023
	38		23		0.03	1.5	0.057
	37		27		0.04	2.2	0.081
	35		30		0.05	3.1	0.109
	33		33		0.06	4.2	0.140
	32		37		0.07	5.5	0.175
	30		40		0.08	7.1	0.213
	28		43		0.09	8.9	0.252
	27		47		0.11	10.9	0.292
	25		50		0.12	13.3	0.331
	23		53		0.14	15.8	0.369
	22		57		0.15	18.6	0.404
	20		60		0.17	21.7	0.435
	18		63		0.18	25.1	0.460
	17		67		0.20	28.7	0.478
	15		70		0.21	32.6	0.489
	13		73		0.23	36.7	0.489
	12		77		0.24	41.1	0.479
	10		80		0.26	45.7	0.457
	8		83		0.28	50.5	0.421
	7		87		0.29	55.5	0.370
	5		90		0.31	60.8	0.304
	3		93		0.32	66.3	0.221
	2		97		0.34	71.9	0.120
	0		100		0.36	77.8	0.000

Result

Navier: Design forces in the critical=20 cross-section
	Eccentricity e_Res =3D 20 mm	Normal forces (vertical load)	n_Res =3D 50.40 kNm/m
	Moment m_d =3D n_Res =C3=97=20 e_Res	m_d =3D 0.98 kNm/m
Navier: Moment capacity at n =3D 50.40 = kN/m (see=20 n-m-diagram)	m_u =3D 0.34 kNm/m
Navier: Utilization ratio UR =3D = m_d /=20 m_u =3D 0.98 / 0.34 =C3=97 100%	UR =3D 285 %

Ritter: Design forces in the critical=20 cross-section
	Eccentricity e_Res =3D 19 mm	Normal force	n_Res =3D 50.60 kNm/m
	Moment m_d =3D n_Res =C3=97=20 e_Res	m_d =3D 0.94 kNm/m
Ritter: Moment capacity at n =3D 50.60 = kN/m (see=20 n-m-diagram)	m_u =3D 0.42 kNm/m
Ritter: Utilization ratio UR =3D = m_d /=20 m_u =3D 0.94 / 0.42 =C3=97 100%	UR =3D 224 %

Conclusion: The load capacity is NOT adequate.

Comments
	Vertical supporting walls is partially supporting the = horizontal load.=20 The proportion supported can be calculated through the module=20 "Horizontal loaded walls". The proportion supported between = horizontal supports is labelled the equivalent horizontal=20 load.

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