Your research library, reconstructed.

One workspace for every paper, book, and standard you read. Collect, read or listen, annotate, search, and cite, with scans rebuilt into clean text that remembers the page it came from. It runs on your computer and syncs privately to the web.

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4.3 Differential equation of the deflection curve

Consider a prismatic beam of flexural rigidity EI carrying a distributed load q(x). Taking moments about a section at x and letting the element length tend to zero gives the governing relation between load and deflection w:

E I \frac{d^{4} w}{d x^{4}} = q (x)

(4.12)

Fig. 4.7 Simply supported beam under distributed load.

Support	Conditions
Simply supported	w = 0, w″ = 0
Clamped	w = 0, w′ = 0
Free	w″ = 0, w‴ = 0

Heading

4.3 Differential equation of the deflection curve

Paragraph

Formula

E I \frac{d^{4} w}{d x^{4}} = q (x)

EI\,\frac{d^{4} w}{dx^{4}} = q(x)

Figure

Fig. 4.7 Simply supported beam under distributed load.

Table

Support	Conditions
Simply supported	w = 0, w″ = 0
Clamped	w = 0, w′ = 0
Free	w″ = 0, w‴ = 0

Tap or hover a region on the scanned page to see where it came from. Every block keeps its page and bounding box.

HOW IT WORKS

From a folder of PDFs to a library you can think with.

1
Collect

Drop in PDFs and scans, or follow feeds and let new work come to you. Docr’d recognizes each document, fills in its details, and catches files you already have.
2
Read

Read scans as clean text beside the original, or listen while a local voice reads aloud. Highlight, comment, and pick up exactly where you left off.
3
Connect

Write notes that link back to the exact page, map references and citations, and line up what your sources say in outlines and syntheses.
4
Cite

Copy a formatted citation, or export a cited draft to the tools you write with. Your library is always yours to take along.

FEATURES

One workspace, a place for each kind of work.

Docr’d is organized the way research actually goes: reading, filing, note-taking, exploring, arguing, and keeping up. Each has its own place in the rail, one click away, in the order you choose.

HOME

Open to where you left off.

Home gathers the documents you have open, the work on your desk, and what arrived while you were away, so the first click of the day goes straight back into the work.

Continue reading reopens every document at the page you stopped on.
On the desk keeps your research maps, outlines, and syntheses within reach.
The last seven days at a glance, with a dot for everything you read, wrote, or added, and a logbook where every line opens the thing it names.

Logbook this week

readwrittenimported & found7 days · 15 events

09:14ReadBeam theoryp.142
08:50FoundNonlinear beam modelsFeeds
TueWroteBeam deflectionNotes
TueEditedThesis, chapter 3Outlines

READING

Read it, or have it read to you.

Switch any document between the original PDF, a split view, and clean reflowed text. When your eyes need a rest, a local voice reads aloud and the page follows along.

PDF, Split, and Document layouts, with the original page next to its reconstruction.
Read aloud in the web and desktop apps with a voice that downloads once, then runs on your device. Choose a voice and speed, step sentence by sentence, and resume where you stopped listening. Document text is never sent to a voice provider.
Highlights, underlines, and strikeouts in your own colors, each with a comment. Turn the passage being spoken into a highlight without stopping.
Clip any area of a page, such as a figure or a derivation, and cite it in your outlines and syntheses.
Every tab, page, and zoom comes back exactly as you left it, alongside the outline, thumbnails, and your private bookmarks.

Consider a prismatic beam of flexural rigidity EI carrying a distributed load. Taking moments about a section and letting the element length tend to zero gives the governing relation between load and deflection. The constants of integration follow from the conditions at the supports.

Your note p.142

Same argument as the string derivation in Strogatz, ch. 12. Compare boundary conditions.

‹› Reading aloud Heart · 1× Annotate spoken passage

RECONSTRUCTION

Old scans become text you can search, copy, and correct.

A photocopied chapter or a forty-year-old standard turns into clean, selectable text, with the equations, tables, and figures kept as real objects rather than pictures.

Formulas come back as editable math. Copy the LaTeX or search for a formula by typing it, and export the whole document as Markdown or LaTeX.
Tables become real tables, merged cells included, and figures keep their captions.
Every line remembers exactly where it came from, so one click jumps back to the spot on the page.
Check any formula or table against the original crop and fix it in place. Your corrections carry through to search and exports.
Every paid plan includes monthly OCR pages in Docr’d Cloud, at Fast, Balanced, or Max quality. If an allowance runs out partway through a book, the finished pages are kept and the rest continues later.

Formula p.142

E I \frac{d^{4} w}{d x^{4}} = q (x)

EI\,\frac{d^{4} w}{dx^{4}} = q(x)

Table p.143

Simply supported	w = 0, w″ = 0
Clamped	w = 0, w′ = 0

Figure p.142

LIBRARY

Drop it in. Docr’d files it.

Add a PDF or a scan and the details fill themselves in. Your library stays tidy without you tidying it.

Papers and books are recognized on import from their DOI, ISBN, or arXiv ID, and their title, authors, and year fill in automatically. Standards are read from their designation and offered for your review.
The same file added twice is caught before it clutters your library.
Binders work like playlists. One document can live in as many as you like.
Nested tags with aliases, so "ML" and "machine learning" mean the same thing.
Document groups keep editions and companion documents together, and any search can be saved to reuse later.

Drop PDFs and scans here

Nonlinear Dynamics and Chaos Strogatz, 2015 textbookdynamics
Attention Is All You Need Vaswani et al., 2017 machine learningto read
Design of Steel Structures, 4th ed. Details found from ISBN structures

NOTES

Notes that link back to the page.

Write in plain Markdown with math when you need it. Every note knows which passages it came from, and every document knows which notes mention it.

Quote a passage into a note and the citation and page number come along.
Link notes to each other with double brackets. Backlinks appear on their own.
A link can reopen the exact page and region of a document, even from another app on your desktop.
Browse every highlight and comment across your whole library in one view.
A note keeps its last fifty revisions, so you can always go back to what you wrote.

Beam deflection

The governing relation is the fourth-order form of [[Euler–Bernoulli beam theory]]. Boundary conditions decide everything downstream, see the table on p. 143.

"Taking moments about a section and letting the element length tend to zero…" Beam theory, p. 142

Linked from

Thesis outline, chapter 3
Reading list: structures

One search across everything you have read.

Titles, full text, your notes, your highlights, figure captions, table contents, and the math itself, all answered from a single search box.

Search inside scans as easily as inside born-digital PDFs, and across binders, research maps, outlines, syntheses, and feed articles too.
Type a formula the way you would write it and find every place it appears.
Narrow by title, author, tag, binder, or type of result.
Results open at the exact page and highlight what you searched for.
Save a search and it keeps itself up to date. Type › and the same field becomes a command palette.

RESEARCH

Find what to read next.

Start from any paper in your library and explore its references, the work that cites it, and related research on a map you can move around.

See references, citing papers, and similar work for anything you have saved.
Read abstracts, authors, and citation counts without leaving your library.
Save a paper you find and its details are already filled in.
Name a map to keep it, step back through your exploration, and pick up a different thread.

OUTLINES AND SYNTHESES

Build the argument from the evidence.

Turn what you have read into something you can write from. Every claim stays attached to the highlight, formula, table, or figure that supports it.

Evidence outlines arrange your highlights and notes into an argument, one claim at a time.
Syntheses compare what each source says, theme by theme, in a single matrix.
Every cell cites back to the exact passage, so one click returns you to the source.
Export an outline as a cited Markdown draft with page locators, ready for pandoc.

	Governing equation	Shear deformation
Timoshenko, 1961	Fourth-order relation between load and deflection. p.142 · (4.12)	Neglected for slender members. p.151
Nonlinear beam models, 2019	Adds axial stretching for large deflections. p.6 · Fig. 2	Included through a correction factor. p.9 · Table 1

Shear deformation matters once the beam is
no longer slender [@timoshenko1961, p. 151].

FEEDS

New work finds you.

Follow the journals, authors, and questions you care about. New articles arrive in one inbox, ready to save or dismiss.

Watch RSS and Atom feeds, authors, saved queries, binders, and research maps.
Hear about it when something in your library is retracted or corrected.
Turn on hosted checks and your watches keep running while your computer is closed, within a daily ceiling you set.
Save an article to a binder with its details already filled in. Subscriptions move in and out as OPML.

CITE AND EXPORT

Cite in a click. Leave whenever you like.

Your citations are ready in the style you need, and your whole library can walk out the door in formats any other tool understands.

Copy a citation in any of 14 bundled styles, from APA and IEEE to Nature, or install your own CSL style.
Export references as BibTeX, BibLaTeX, RIS, or CSL JSON.
Turn a reconstructed document into clean Markdown with its figures, or into a complete LaTeX project ready to compile.
Save a copy of any PDF with a proper, navigable table of contents added.
Export your entire library, notes and highlights included, in files you can open without Docr’d.

APA

Timoshenko, S. (1961). Theory of elastic stability (2nd ed.). McGraw-Hill.

BibTeX

@book{timoshenko1961,
  author    = {Timoshenko, Stephen},
  title     = {Theory of Elastic Stability},
  publisher = {McGraw-Hill},
  year      = {1961},
  edition   = {2}
}

Markdown
LaTeX project
BibTeX
BibLaTeX
RIS
CSL JSON
PDF with outline
Library bundle

CLOUD AND SYNC

Pick up exactly where you left off.

Your library, highlights, notes, and reading positions stay in step across your devices. Close a paper on your desktop and it is waiting on the same page in your browser.

Your library, notes, and highlights sync across your devices. PDFs download when you open them, or pin the ones you want offline. Linked files stay on the computer that has them.
Desktop sync encrypts your data before it leaves your computer. To let you restore on a new device just by signing in, Docr’d keeps a recovery key, so this is not end-to-end encryption. Read about privacy.
The desktop app works without a connection. Your changes catch up the next time you are online.
Prefer to keep everything on one computer? Use the desktop app without signing in.

THE NEXT CHAPTER

Make room for your research.

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