Chapter 1. A Vertical Tensile Structure
The concepts of force, free-body diagrams, static equilibrium in a
single direction, tension, and stress are introduced through study of a weight hanging on
the end of a wire. Steel hanger straps for a10-floor building are designed and detailed as
a vehicle for applying these concepts to a tangible design problem. Sidebars introduce SI
metric units and discuss numerical accuracy. The final illustrations are photographs of
actual hangers in an office building and a tied-arch bridge.
Chapter 2. A Vertical Compressive Structure
A stack of stone blocks is analyzed to introduce the concepts of
compression, dead load, elementary graphical analysis, buckling, and invertibility. These
concepts are put to work by sizing concrete columns for a tall building, noting how column
size changes from top to bottom. Sidebars demonstrate why mosquitoes have proportionally
thinner legs than elephants, and show the theoretical maximum limits on heights and spans
of structures.
Chapter 3. Forces in Many Directions
Force vectors and vector addition by means of force parallelograms
and tip-to-tail addition are introduced in both numerical and graphical examples, along
with static equilibrium of concurrent forces in a plane. As a useful example, the sloping
tension straps and struts at the top of the building developed in Chapter 1 are analyzed
and their construction details are sketched. Then simple graphical manipulations are used
to discover ways of reducing the forces in these members by changing their geometry.
Chapter 4. Moments of Forces
Moments of forces are defined, and the final equation of static
equilibrium in a plane is introduced. A number of beam reactions are calculated. Truss
member forces are found numerically by the method of joints. A couple is defined and
evaluated. A sidebar reviews the essential features of a free-body diagram.
Chapter 5. Finding Forces in a Simple Truss
This entire chapter is given to analysis of triangular single-panel
trusses through both numerical and graphical methods. Students learn the effects of
changing the magnitude of the external load, changing the depth of the truss, adding a
kingpost, inverting the truss, and applying an inclined load. A sidebar shows alternative
ways to transfer parallel lines, an essential operation in graphical solutions.
Chapter 6. Multipanel Trusses
In solving for the forces in a six-panel truss, this chapter
introduces for the first time a complex graphical solution. Then, through graphics, it
demonstrates the effects of reversing the direction of the diagonals of this truss,
diminishing its depth, changing its shape to a triangle, changing to an odd number of
panels, and applying an asymmetrical loading. Cantilever and overhanging trusses are
analyzed and common truss configurations are shown. A preliminary design and details are
prepared for a highly irregular wooden truss for a summer camp assembly building. A long
sidebar discusses hinges, rockers, rollers, and fixed end conditions and depicts actual
examples of each.
Chapter 7. Fanlike Structures
Graphical solutions for fan, harp, and half-harp or semifan cable
stay configurations are presented, and are shown to be identical to truss solutions.
Erection procedures and details are presented for cable-stayed bridges and roofs. A small
cable-stayed footbridge is designed from scratch. Compressive fan structures, which are
the inversion of cable-stayed structures, are presented through analysis of two actual
structures of this type. Santiago Calatrava's daring Alamillo Bridge is analyzed
graphically to determine how much its backward-leaning tower must weigh in order to
maintain equilibrium. An irregular stay rod arrangement for the roof of a famous high-tech
building is analyzed.
Chapter 8. Finding Form and Forces for Funicular Structures
Through both numerical and graphical analysis of a hanging string
with a very irregular loading, students are shown how to find the forces in a hanging
cable. This introduces the concept of funicular form and families of funicular forms. The
fundamental graphical method for finding form and forces for cables and arches is
developed. The Dulles Airport hanging roof is analyzed, after which form and forces are
found for a concrete deck-stiffened arch bridge. A sidebar shows how to make live and dead
load estimates.
Chapter 9. Further Design Tools for Funicular Structures
Further variants of the graphical construction for funicular shapes
are demonstrated. One of these allows students to construct a funicular curve through any
three designated points. This is applied to the shaping of an arch for an earth-filled
bridge, in which the dead load is not uniformly distributed. A numerical method is also
developed for finding a curve through any three points. Graphical constructions are
demonstrated for finding resultants of groups of forces and finding beam reactions. A
numerical method for designing uniformly loaded (parabolic) cables and arches is derived
and demonstrated. The history of graphic statics is summarized in a sidebar.
Chapter 10. Shaping a Cantilevered Arch Roof
This chapter begins with a fuzzy sketch of an idea for a
cantilevered concrete shell roof for a stadium grandstand, and ends with every component
of the structure shaped, sized, and detailed, and a rough plan for erection prepared. The
incredible power of graphical methods is especially evident in this chapter, although
numerical solutions are also presented. Discussions of detailing and construction
procedures bring to light a plethora of valuable information on concrete construction.
Chapter 11. Shaping a Hanging Roof
This chapter also begins with a fuzzy sketch and ends with a fully
worked out preliminary design, this time for a suspended roof over an auditorium. The
graphical solution requires no new tools, but the numerical solution requires a new set of
equations for asymmetrical parabolas, given the differing heights of the masts. Means of
restraining the cable against nonuniform loads are presented and discussed. A cable size
is selected, and the fittings, connections, masts, and deck are detailed. Cable lengths
are calculated. Several real cable-hung roofs are shown.
Chapter 12. Shaping a Three-Hinged Truss Arch
Once again, a fuzzy conceptual sketch for an asymmetrical arch
becomes a real building in the course of this chapter. A new set of mathematical
expressions, based on curvature of a parabola, is developed and applied to this project.
Through a combination of graphical and numerical tools, the effects of unbalanced loadings
are evaluated and the resulting stresses in the truss members are calculated. Typical
details are sketched. Several similar but real structures are illustrated, and a sidebar
compares fixed, two-hinged, and three-hinged arches.
Chapter 13. Restraining Funicular Structures
Moving loads, construction loads, wind, and drifting snow can apply
loading patterns for which an arch or cable is not funicular. Through clear diagrams and a
breathtaking array of photographs of great structures from around the world, the student
learns alternative means for dealing with this problem.
Chapter 14. Shaping Efficient Trusses
First numerically, and then graphically, students learn to turn
truss analysis around so as to find forms of trusses that have desired structural
properties. These constant-force trusses are both efficient and elegant, as evidenced by
the numerous photographs of real structures, the most famous of them the Eiffel Tower,
that use them in their various forms. Thus the book ends with a strong emphasis on shaping
structures for both optimum performance and inherent beauty.
Unit conversions
Standard sizes of steel reinforcing bars
Selected References
Index
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