Teaching Efficiency in Ribbed Forms with Paper Vaults

Abstract

This is an in-class activity that uses a piece of paper and weights to demonstrate how ribbing in a vault is an efficient form, and to help students understand the important role of corrugations and form in the stiffness of a vault.

Learning Objectives

After this activity, students should be able to:

  • Demonstrate that ribbing can increase the stiffness of a vault without adding thickness
  • Recognize the importance of Nervi’s ribbed vaults
  • Explain how load is carried more efficiently in a corrugated form

Background

Ribbed vaults have appeared in historical structures for centuries. For example, the Pantheon and the Vatican Museum utilize the stiffening effects of ribs in the dome vaults. Pier Nervi was a modern engineer whose inspiration came from the ribbed vaults of Gothic architecture. Utilizing innovations in construction, Nervi developed construction methods that made his shells both feasible and economical. For the Little Sports Palace, Nervi used precast diamond ‘pans’ and cast-in-place ribs.

The concentration of the ribs at the support points act as inclined buttresses and allow for the openings along the base of the shell since the forces can flow along the ribs. 

In this activity, students work in groups to understand and experience the efficiency of ribbing in vaults. Through their explorations, students discover that incorporating corrugation can increase the stiffness of a vault.

Materials List

  • For each group: one piece of letter size paper (plain or cardstock) with pattern, 4 textbooks, weights (books, or ream of paper).

Procedure

First, we can demonstrate the efficacy of adding corrugation in one direction. A sheet of paper can be suspended between two supports. If it were to support a significant weight, such as a can of beans, the paper would immediately collapse. However, if we add a simple corrugation (series of folds in one direction), we can dramatically increase the stiffness of the sheet of paper and it can support a can of beans. This is the principle behind corrugated cardboard and corrugated metal structures such as corrugated tin roofs.

can on books

We can create even stronger structures out of a single sheet of paper by adding corrugations in two directions. A paper vaulted barrel is an example of such a structure.

folded paper pattern

Following the pattern on the paper, fold up along dotted lines and fold down along solid lines, ensuring crisp folds. Buttress ends of vault using 2 supports (e.g. heavy books) on either side.

paper barrel

paper holding book

Before loading the shells, have the students predict how many times its self-weight it can hold. 

Students then perform the activity. Once the vaults have been folded, have the students weigh the vault. Have students load the shell with reams of paper or books and report the maximum amount of weight the shell held. 

Finally, have the students summarize what they learnt from this activity with a question or discussion about the general conclusions. The responses to this question can be used to assess the learning objectives of this activity.

From the lecture: Pier Luigi Nervi and the Italian Tradition of Ribbed Vaults

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