Today's Topics

• Diaphragm behavior and idealizations
• Shear wall behavior
• Construction issues

Diaphragm behavior and idealizations

Rigid diaphragms, symmetry, and relative stiffness

All frames equal stiffness

Center frame is twice as stiff All frames equal stiffness

Symmetrically arranged & unequal stiffness means resistance is proportional to stiffness
	When the stiffness of the center frame is doubled compared to the outer frames, it offers twice as much resistance as those frames.
Relative stiffness
	When structural elements are linked so that their displacements are equal, they resist loads in proportion to their stiffness.
Stiffness "attracts load"
	An element which is twice as stiff will carry twice as much load, provided displacements are equal.

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What happens if we stiffen the frame on the right, rather than the frame in the center? How will the loads be distributed?

Third frame is twice as stiff

All frames equal stiffness

Unexpected result
	Stiffening the frame on one end increases the forces in the frame at the other end

Third frame is twice as stiff

Third frame is twice as stiff

Torsion
	Stiffening one end frame moves the center of stiffness away from the resultant of the load, inducing torsion: the structure twists.
Frame displacements are not equal
	With torsion, the displacements of the three frames are not equal
Relative stiffness applies only when displacements are equal
	With torsion, relative stiffness does not apply, forces will not be distributed in proportion to stiffness
Local actions and global consequences
	With rigid diaphragms, a change in one part of a structure can have significant effects on other, possibly remote, parts.

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Real diaphragm behavior

A concrete slab vs. an ideal rigid diaphragm

Concrete slab	Ideal rigid diaphragm
Concrete slab

In a real diaphragm, the displacements are not ideally equal
	The deformation of the diaphragm allows the center frame to deflect more, so each of the outer frames reduces by about 4 kips, so that the center frame gains about 8 kips compared with the ideal.
The Rigid diaphragm assumption can often reasonably approximate a concrete diaphragm
	Reinforced concrete floor slabs and concrete-topped steel deck can often be reasonably approximated by rigid diaphragm behavior, provided that diaphragm is significantly stiffer than the vertical frames or shear walls

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A plywood diaphragm vs. an ideal rigid diaphragm

Plywood diaphragm	Ideal rigid diaphragm
Plywood diaphragm

With a plywood diaphragm, the force distribution is very different from the rigid diaphragm
	The deformation of the diaphragm allows the center frame to deflect more, so each of the outer frames reduce 20 kips, so that the center frame gains nearly 40 kips, compared with the ideal rigid diaphragm.
The rigid diaphragm assumption poorly approximates a plywood diaphragm
	The plywood diaphragm is very flexible relative to the frames.
Tributary width is a better idealization
	The distribution of loads to the frames is close to the tributary width assumption, with approximately half the load going to the center frame, and one quarter each to the outer frames.

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What happens to the wood and concrete diaphragms if we stiffen one of the end frames? How will it influence the distribution of forces in each case?

Real diaphragms and unsymmetric stiffness

Plywood diaphragm	Concrete diaphragm
Plywood diaphragm	Concrete diaphragm

Timber: frame stiffness has little effect on the distribution of forces.
	The diaphragm is not stiff enough to make the building twist as a unit. Each panel deflects like a simple beam, distributing approximately half of its load to each end, regardless of the stiffness of the frame.
Concrete: frame stiffness has much more influence on the distribution of forces.
	The behavior is much closer to the ideal rigid diaphragm, where the twisting action induces larger forces in the end frame that is not stiffened.

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Relative Stiffness of diaphragm and vertical elements

 

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Lessons

Irregular distribution of stiffness is an important concern for rigid diaphragm buildings.
	Adding stiffness to one portion of a rigid-diaphragm structure can cause induce torsion, resulting in significant problems in other parts.
Concrete is typically modelled as a rigid diaphragm
Plywood and bare steel deck are typically modelled as flexible diaphragms

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Shear Walls