• Tri-dimensional surfaces

• Resist loads through their geometry

• Self supported structures

• No additional columns or frames needed

• Grid pattern replaces the shell material which enables the overall structure to

benefit from the combined action of shell and arches and thus to achieve unique

shapes.

• Same structural behavior as shells, gain their stability from their geometric shape

• Internal forces are carried by members and therefore have to follow a restricted

number of paths.

• A plain, continuous shell can resist

normal and shear forces while the

lattice shell can only resist forces in

the direction of the lath i.e. axial

forces.

• The grid was initially flat and the structure was later

raised into its doubly-curved shape.

• The forces transformed the square grids into similar

parallelograms causing the diagonal lines through

the nodes to change.

• Aesthetics required the cross-section of the laths be

50mm x 50mm.

• Increased lath size also increased the initial bending

stress.

• Engineers decided to double the laths one above the

other creating four - rather than two - layers of

wooden laths.

• Four layers of laths complicated the construction scheme

• Members needed to rotate and slide between two

parallel laths during the erection process, creating the

parallelogram cells.

• For this, a pinned connection was needed between the

middle two laths and slotted holes were needed in the

outer layers to allow for this movement

• During its erection, the grid is pushed up from

below using scaffolding towers, which induce

bending stresses in the laths.

• After the mesh is lifted into shape, the

boundaries must be fixed.

• The pins were tightened with node bolts to

retain the shape.

• Addition of blocking pieces, known as shear

blocks, between parallel laths increased the

shell's overall stiffness.

• Although the out of plane shear stiffness was

provided by bolting and shear blocks, steel cable

ties were needed to provide the diagonal

stiffness to the shell.

• Steel cables of 6mm diameter were tied and

stressed by inserting a small block of steel

between two parallel cables

Hanging chain model

• When a uniform distributed load is

applied to a suspended line, it

naturally shapes itself so as to be

free of bending moments.

• Chains remain fully in tension

• Once inverted, all the internal

forces act in compression.

• Minimized shear forces.

• The Mannheim Multihalle spans 85 meters and contains 7400 m2 of roof area,

but its shell thickness is less than half a meter.

• The ratio of the thickness of the shell to the span is approximately .00625 which

means that the structure is proportionately thinner than an eggshell!

• The completed roof structure weighs only 16 kg/m, much lesser than an average

concrete plain shell.

• The out of plane shear stiffness was provided by bolting and shear blocks while

steel cable ties provided the diagonal stiffness to the shell.

• The forces flow down to the boundary of the mesh, where the structure has a

concrete boundary.

• The laths are connected with bolts to a wooden board that is set at the correct

angle and connected to concrete blocks using steel brackets.

• The boundaries at locations where there are openings were either arches or

laminated timber beams which provide the necessary resistance to the lath force

without increasing edge thickness, which are often connected to columns.

• A simplified structural analysis was performed.

• Two forces need to be considered:

• The initial force (Pinitial) required to begin deflecting a lath,

• The subsequent force (P) required to keep the lath deflected once it is in

place, to be referred to as the "lift force."

• These two forces were determined (without considering the lath's self-weight)

using Timoshenko's elastic stability theory

P= Force needed to maintain bent shape of lath

• Since the elastic stability theory deals with a cantilevered beam, only half the arc

length of the Multihalle was considered. Therefore, l is defined in Equation 1 as:

(1)

• where L = 80m, and l = 40m. Given this value of l and angle of deflection α of 60

degrees for the Multihalle (based on the arc length and the Multihalle's estimated

height of 20 m), the elastic stability theory allows for an estimation of the elliptic

integral B that can be used to solve for the lift force P.

• For the dimensions of the Multihalle, B = 1.686. Using B, k can be solved by

substituting Equation 3 into Equation 2:

(2)

(3)

which, when combined, yield Equation 4 to solve for the lift force P:

(4)

• The initial force Pinitial can be solved using Equation 5:

(5)

• Specificity of the construction scheme requires members to be flexible enough so

that they can deform during the construction phase.

• Materials with a large Young's Modulus, such as steel (E = 210 GPa), are stiffer

and require a greater Pinitial and P because more force is needed to bend them.

• Materials with a smaller Young's Modulus, such as wood (E~10 GPa) and

aluminum (E = 69 GPa), are more flexible and require a smaller Pinitial and P

because they bend more easily.

• The capacity of timber to bend without braking and to remain elastic makes

timber a material of choice.

• It is important to note the significant increase in initial force, Pinitial, that occurs if

the shear blocks are introduced before erection, due to increased moment of

inertia.

• For wood, for example, the initial force increases from 0.04 kN to 0.92 kN if the

shear blocks are placed prior to erection, which is a significant difference.

• These values confirm the ingenuity of the erection process used to construct the

Mannheim Pavilion, since the process reduced the overall lift force required

without sacrificing the shell's final stiffness.

• Once these forces were determined, the stresses experienced by the shell were

calculated under four different load cases:

• The lift force required to erect the shell lattice

• The self-weight of the lattice

• The design snow load

• The design wind load

• For the first and second load cases: (6)

where Ia is the moment of inertia of a single lath, since these load cases are resisted by individual

laths before they become connected via shear blocks, and ya is equal to 0.25m (perpendicular

distance from the edge of a lath to its neutral axis).

• The equation used to calculate the stress of the laths in the third and fourth load

cases is the following:

(7)

where Ib is the moment of inertia of two connected laths, joined by a shear block, since these load

cases are resisted by the shell as a whole once the shear blocks are in place, and yb is equal to 0.75m

(perpendicular distance from the edge of a lath to the neutral axis of the combined laths and shear

block).The area is twice as large in this instance because the stress is shared by two laths that are now

connected.

• Considering that the compressive strength of hemlock is 46.7 MPa, the maximum

stresses created by the design loads (~25 MPa) is less than what this type of

wood can resist.

• The cost of the multipurpose hall was relatively low compared to other typical

building projects at the time.

• The Mannheim Pavilion is impressive not only for its unique construction process,

but also for its design durability despite the technological limits of the time in

which it was envisaged and realized.

• The Mannheim Multihalle is a physical proof that little more than simple math

and a detailed model could be used to create a structure with both organic

materials and form.

• The design of grid shells structures both in the form finding process and in the

prediction behavior of the building under operation appears to be a complex

process.

• Contrary to other more common structural systems no design guide lines exist

and no tools have been developed specially for their study until now and the

engineers have resorted to techniques such as chain form finding test their

designs.

• The fact is, that the lack of expertise in this field is a hindrance to the further

development of grid shells.