Simplified Reinforced Concrete Mathematics by Melvin D. Casler develops working formulas for reinforced-concrete members and demonstrates aids intended to reduce calculation. Published in New York by D. Van Nostrand Company in 1915, its subtitle describes the derivation of formulas and their application to beams, columns and arches, with a nomographic computing device.
What the author wanted to simplify
The preface identifies two linked aims: obtaining practical working formulas and applying them with fewer laborious computations. Casler discusses members subject to longitudinal stress together with bending, including eccentrically loaded columns and arches.
He also warns against using special tables and curves blindly without understanding their limitations. That qualification is useful when reading the volume today. A calculating aid can save time while still depending on assumptions that the user must understand.
The book is therefore both a mathematical explanation and a record of engineering calculation practice. It shows how an author tried to make repeated work more manageable without removing the need to check whether a method fits the problem.
Derivation of formulas
The first chapter begins with diagrams illustrating general principles. Nomenclature and signs are stated before assumptions and fundamental formulas are introduced. This sequence establishes the meaning of the quantities used in the later examples.
Beams and slabs receive formulas of their own, followed by formulas for combined stresses. The contents also identify a group of formulas for beams and slabs and a group dealing with longitudinal compression combined with transverse moment.
For a reader studying historical technical literature, the value lies in following the reasoning rather than extracting an isolated expression. Symbols, sign conventions and material assumptions all affect what a formula means. The introductory diagrams provide an important bridge between the words and the algebra.
Labor-saving diagrams and a slide rule
The second chapter turns to labor-saving devices. A circular diagram for simultaneous evaluation of variables, rectangular coordinate curves and a table of corresponding values appear among the aids. The author then describes a reinforced-concrete slide rule and demonstrates its use.
These pages are especially interesting as a history of computation. They show relationships being arranged visually and mechanically so that repeated numerical operations could be performed more efficiently. The device is part of the argument about practical calculation, not an unrelated illustration.
Readers can compare the different forms of aid and consider what each makes easy to see. A curve, table and slide rule organize information differently, even when they arise from related formulas. Understanding those differences helps explain the author’s emphasis on flexibility.
Worked examples for different members
The illustrative-examples chapter gives a systematic procedure for typical beam problems. It includes designing a beam and slab, investigating stresses in a given beam, computing safe load and finding the steel in a beam of known dimensions.
Further examples address the dimensions of a beam containing a known area of steel, design under combined longitudinal stress and transverse moment, and an eccentrically loaded column. The final example concerns a reinforced-concrete conduit illustrating figures and an arch ring.
This range shows why Casler sought a method that could handle more than one narrowly defined case. The examples move between determining dimensions, checking an existing section and examining different combinations of action. They are historical demonstrations rather than current ready-to-build designs.
General notes and interpretation
The last chapter provides general notes on reinforced-concrete design. It discusses questions of practice and problems for which definite mathematical rules are difficult to formulate, and includes a web-reinforcement discussion. These notes place calculation within a broader design process.
The volume will interest engineering historians, students comparing older analytical methods and readers studying nomography or slide-rule calculation. Present-day structural decisions require current theory, codes and professional assessment; the book’s assumptions and examples belong to its 1915 context.
Digital format
This free ebook contains 74 PDF pages, including preliminary matter and diagrams. It is an image-based scan without searchable text. The contents near the beginning list the formula derivation, computing aids, examples and general notes. Use the printed page numbers to navigate, and examine symbols and graph labels directly on the scanned page when following an argument.
Book details
- Author: Melvin D. Casler
- Publisher: D. Van Nostrand Company, New York
- Year: 1915
- Edition: No numbered edition stated
- Digital length: 74 PDF pages
- Language: English
- File size: 0.72 MB
