ceng 232 l7 - out-of-plane walls

L7 - Rigi(ty, Out-of-Plane Walls

CENG 232 - Winter 2015 1

Wall Rigidity and

Out-of-Plane Walls

CENG 232 Lecture 7

Shear Wall Rigidity (Text 3.8.2)

For buildings with rigid diaphragms, lateral loads are distributed based on relative stiffness of walls

Wall rigidity is the shear required to cause a unit deflection of the wall:

R = V


Deformations are due to: Flexural deformation Shear deformation Foundation rotation or uplift

Assuming the shear wall is a deep cantilever beam:

Youngs Modulus:

Shear Modulus:

=VH 33EmI

+1.2VHAEv

+ F2HL

Em = 900 f mEv = 0.4Em

Foundation rotation is usually ignored


For distribution of EQ loads, only the relative rigidity is needed.

For walls with the same thickness, relative rigidity is:

The force resisted by each wall is:

Ri =1

4 HL

3+ 3 HL

i

Vi =RiRi

i=1

n

V




If the top of the wall is restrained from rotation (fixed-fixed):

For walls with the same thickness, relative rigidity is:

=VH 312EmI

+1.2VHAEv

Ri =1

HL

3+ 3 HL

i Load to each shear wall can be calculated

based on relative stiffness.

Determining relative stiffness can be more difficult for walls with openings like this

The walls of this school have architectural CMU veneer over loadbearing CMU.



Varying wall stiffness in a CMU building

Rigidity of Walls with Openings (Text 3.8.2)

Modified stiffness for walls with openings:

wall = solid wall solid strip + piers

Example 3.8.3: Rigidity of Walls with Openings

Wall broken into 6 segments

Relative rigidity found for each

30 kip force is distributed according to relative rigidity

Example 3.8.3: Rigidity of Walls with Openings

Solution:



Out-of-Plane Loads on Walls (Text 3.9)

Shear walls loaded out-of-plane are not part of the lateral-load resisting system, and need only support their own loads.

Because wall deflections are comparable to the wall thickness, P- effects must be considered.

Christchurch, New Zealand, 2011. An example of out-of-plane failure of an unreinforced masonry wall.

Christchurch, New Zealand, 2011. Failure of an reinforced masonry wall.

Out-of-Plane Loads on Walls (Text 3.9.1)

Out-of-plane EQ loads different for structural and non-structural walls.

Structural walls: part of lateral load resisting system

SDS = design spectral response acceleration in short period range

I = importance factor

Wp = weight of wall

Fp = 0.4SDS I Wp

Non-structural: see text section 3.9.1 for loads

Fp min = 0.1 Wp



Walls can be designed to span vertically, or horizontally between vertical supports:

Out-of-Plane Loads on Walls

Effective wall height for design is based on supports:

This wall is being braced while under construction to reduce its effective height.

Out-of-Plane Analysis of Slender Walls (Text 5.5.1)

Out-of-plane wall design MSJC requirements valid if one of the following is satisfied:

Pu = factored axial load at location of max moment

Ag = gross cross-sectional area

H = effective height of wall

t = wall thickness

Pu 0.05 f m Ag0.05 f m Ag < Pu 0.20 f m Ag;

H t 30




Equations based on pinned-pinned walls. Use equivalent span for non-pinned walls.

Wall moments due to: Lateral loads (w) Eccentricity of floor loads (Pf) of wall weight x parabolic

shape deflection (Pw x 2/3)

(assumes parabolic deflected shape, with top of wall c.g. at 2/3 of )


Moment at the middle of the wall is:

Note that the wall moment is based on the wall deflection (), which is based on the wall moment.

(an iterative process)

M = wH2

8 +Pf e2 + Pf + Pw( )

Cracked Section Properties:

Cracked moment:

Cracked moment of inertia:

Mcr = Sn fr See Table 1.6.2 for fr

Icr = nAse d c( )2 +bc33

n = modular ratio

Ase =P + As fy

fy

Out-of-Plane Analysis: Closed form solution for wall deflection

(Text 5.5.1)

Substitute wall moment equation into deflection equation to get closed-form (no iteration) solution for deflection:

=

wH 28 +

Pf e2

Mcr 1

IcrIg

48EmIg5H 2 Pw + Pf( )

=

wH 28 +

Pf e2

48EmIg5H 2 Pw + Pf( )

Uncracked: Cracked:

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Design of Slender Walls (Text 5.5.2)

After wall displacement and corresponding moment are determined, the section can be designed.

Design requirements: Out-of-plane moments including P- effects: Horizontal deflection at mid-height under service

(unfactored) loads, s, must be less than 0.007H.

Mn Mu


One layer of reinforcing:

Mn = As fy + Pu( ) d a2

a = As fy + Pu0.8 f mb


Two layers of reinforcing:

Mn = As fy + Pu( ) d a2

Pu d

t2

a = As fy + Pu0.8 f mb

Design of Slender Walls: Effective Width

Maximum width of compression block is the smallest of: 1. Center to center of bar spacing 2. 6t (t = wall thickness) 3. 72 inches

For partially grouted walls, compression zone cannot include the ungrouted part of the wall. Calculate T-beam shape compression block.



Design of Slender Walls: Max Reinforcement

Strain in the reinforcing steel must be at least 1.5 times the yield strain when the masonry reaches its strain limit.

(see text 5.5.2 for derivation)

max =As,maxbd

max = 0.64 f m

fy0.0025

1.5 fy Es + 0.0025

Pbdfy

where = 1.5, mu = 0.0025

Example: Design of Slender Walls

ceng 232 l7 - out-of-plane walls

Documents

shear walls

openings wall

plane walls ceng

walls effective wall

wall deflections

vshear wall rigidity

nonstructural walls

plane loads