DTI
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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 weight concrete

Input

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

Dimensions
| Height= 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 fcg = 3.50 MPa | Flexural strength ftg = 1.20 MPa | Density = 650 kg/m³
| E-module Ecg = 1600 MPa | |
| Consequence class= Normal | Control class= Normal |

Design loads
| Vertical load (positive downwards) nd = 50.0 kN/m | Topeccentricity (positive opposite horizontal load) e0 = 17 mm
| Eccentric reaction at the footing is accepted.

| Out-of plane eccentricity e5 = 5 mm | Horizontal load (wind) wd = 0.50 kN/m²

General pressumptions

Vertical loaded storey high walls of light weight concrete

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

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

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

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

In the un-cracked phase the flexural strength is taking into consideration. The mn-diagram is developed from the extended Navier formula taking the column 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 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
The dead load in the upper part of the wall
Eccentricity in top and bottom ee
Out of plane deviation of the wall
Horizontal load

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

Calculations

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

Effectivce length:

| The reduced column height ls = 1.00 × 2800 = 2800 mm

The slenderness ratio:
| Equivalent column thickness: ts = 100 mm
| ls / ts = 2800 / 100 = 28.0 < 30 => The slenderness ratio is OK

Parameters: | Charac. value | Safety factor | Design value
| Compressive strength | fcg = 3.50 MPa | 1.60 | fcd = 2.19 MPa
| Flexural strength | ftg = 1.20 MPa | 1.70 | ftd = 0.71 MPa

Loads and section forces (design values)
| Moment at the top | Vertical load × Topeccentr. = | mtop = | 0.85 | kNm/m
| Dead load of the wall | | g = | 1.79 | kN/m
| Reaction at the footing | Vertical load + dead load = | Rfod = | 51.79 | kN/m
| Eccentricity at the footing (positive opposite horizontal load) | efod = | -17 | mm

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

Section forces related to Navier-load capacity
| (Critical cross-section is where at maximum moment (in the full length)).
| Resulting eccentricity in the critical cross-section | eRes = | 20 | mm
| Vertical force in the critical cross-section | nRes = | 50.40 | kN/m
| Moment in the critical cross-section | nRes × eRes = mRes = | 0.98 | kNm/m

Section forces related to Ritter-capacity
| (The critical cross-section is pressumed in middle third, at the maximum moment).
| Resulting eccentricity in the critical cross-section | eRes = | 19 | mm
| Normal force in the critical cross-section | nRes = | 50.60 | kN/m
| Moment in the critical cross-section | nRes × eRes = mRes = | 0.94 | kNm/m

Diagram for design load capacities

Navier-capacity:
| Critical normal force: | ncr = Ncr / be = | 60.8 | kN/m
| Factor of second order effect: | mff = | ncr / | (ncr-n)
| Criteria 1: tension stress < tension strength: | mff×σM - σN < | ftd |
| Criteria 2: compression stress < compression strength: | mff×σM + σN < | fcd |

| Normal- | Corresponding failure moment m 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:

| et | td - 2et | ks | 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 cross-section
| Eccentricity eRes = 20 mm | Normal forces (vertical load) | nRes = 50.40 kNm/m
| Moment md = nRes × eRes | md = 0.98 kNm/m
Navier: Moment capacity at n = 50.40 kN/m (see n-m-diagram) | mu = 0.34 kNm/m
Navier: Utilization ratio UR = md / mu = 0.98 / 0.34 × 100% | UR = 285 %

Ritter: Design forces in the critical cross-section
| Eccentricity eRes = 19 mm | Normal force | nRes = 50.60 kNm/m
| Moment md = nRes × eRes | md = 0.94 kNm/m
Ritter: Moment capacity at n = 50.60 kN/m (see n-m-diagram) | mu = 0.42 kNm/m
Ritter: Utilization ratio UR = md / mu = 0.94 / 0.42 × 100% | UR = 224 %

Conclusion: The load capacity is NOT adequate.

Comments

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