Beams

32 standard beam cases: simple spans, cantilevers, propped cantilevers, overhangs, fixed ends and two-span continuous beams. Pick one and it lands on the calcsheet as a schematic plus live functions for its reactions, shears, moments and deflections.

Free on every plan; needs an account.

Find a case

Click the beam icon in the activity bar.

The Beams panel: a search box, the category menu reading Show all (32), and the first two cases with their schematics

Two filters, stacked:

Category (Show all (32)): Simple Beams, Cantilever Beams, Propped Cantilevers, Overhanging Beams, Fixed-End Beams or Continuous Beams.
Search: the letters you type, in order, against name and summary; best match first. It ranks more than it filters – udl keeps 29 of the 32 but leads with the fully loaded spans, and cant point puts Cantilever Beam – Concentrated Load at Any Point on top.

Insert a case

Click the page to place the beacon, then press +. With no beacon it goes below everything.

A uniformly loaded simple beam on the calcsheet: the beam schematic with its name beside it, then R, M max and Delta max as function definitions, each with a description to its right

You get:

The schematic, as a diagram block, with the case name beside it.
One function definition per formula, with a line saying what it gives and where.

It arrives selected, so it drags as one. One Undo removes it. The definitions show no result; they wait to be called.

Choose what comes in

The chevron under + opens the case’s contents, all ticked.

The expanded list for the uniformly loaded simple beam: Include beam diagram, then the typeset signatures R(w, L), M max(w, L) and Delta max(w, L, E, I), each with a ticked box

Include beam diagram: untick it and the name comes in as a small unnumbered heading instead.
One box per formula: hover over one for its description; untick what you don’t need.

Don’t untick a formula the others call. $L_{1}$ , the total length, is the usual one: in Simple Beam – Concentrated Load at Any Point, $R_{1}$ , $R_{2}$ , $M_{ma x}$ and $Δ_{ma x}$ all divide by $L_{1} (a, b)$ . Leave it out and they fail with Undefined function L_1. The panel won’t stop you.

Use the formulas

Define the inputs, then call:

w, L, E and I defined in a row, then R(w, L) = 30 kN, M max(w, L) = 45 kN·m and Delta max(w, L, E, I) = 10.5469 mm

That’s Simple Beam – Uniformly Distributed Load with $w = 10 kN/m$ , $L = 6 m$ , $E = 200 GPa$ and $I = 8000 c m^{4}$ :

R (w, L) = 30 kN M_{ma x} (w, L) = 45 kN \cdot m Δ_{ma x} (w, L, E, I) = 10.5469 mm

Change $w$ and all three move.

Arguments go by position. The first in the brackets is the load, whatever it’s called: M_max(w_d, L_s) works, and so does M_max(10.kN/m, 6.m). While you type, a hint names the argument under the caret and gives a typical value:

The signature hint over a call to M max: M_max(w, L) with L highlighted, and the note that L is the span length, for example 6 m

For all of a formula’s notes at once, right-click its description and choose Detailed Description.

Units look after themselves. The result carries its unit; change it in the unit box, as in Your first calcsheet.

Assign a result to carry it forward. $M_{E d} := 1.5 \cdot M_{ma x} (w, L)$ gives $67.5 kN \cdot m$ .

(Mind $L$ : it’s also the litre. Define $L := 6 m$ and every litre below becomes six metres. Only matters if the sheet measures volumes; call the span $L_{s}$ there.)

The catalogue

Inputs: $w$ a uniform load per unit length, $W$ a total load, $P$ a point load, $L$ a span, $a$ , $b$ and $c$ distances along the beam (the schematic shows from where), $E$ the modulus of elasticity, $I$ the second moment of area. Subscripts number the first and second of a kind. Inputs says what a case needs, not the order; the hint gives the order.

Simple Beams

Case	Gives	Inputs
Simple Beam – Uniformly Distributed Load	$R$ , $M_{ma x}$ , $Δ_{ma x}$	$w, L, E, I$
Simple Beam – Uniform Load Partially Distributed	$L_{1}$ , $R_{1}$ , $R_{2}$ , $M_{ma x}$	$w, a, b, c$
Simple Beam – Uniform Load Partially Distributed at One End	$R_{1}$ , $R_{2}$ , $x$ , $M_{ma x}$	$w, L, a$
Simple Beam – Uniform Load Partially Distributed at Each End	$L_{1}$ , $R_{1}$ , $R_{2}$ , $M_{1}$ , $M_{2}$	$w_{1}, w_{2}, a, b, c$
Simple Beam – Load Increasing Uniformly to One End	$R_{1}$ , $R_{2}$ , $x_{m}$ , $M_{ma x}$ , $Δ_{ma x}$	$W, L, E, I$
Simple Beam – Load Increasing Uniformly to Centre	$R$ , $M_{ma x}$ , $Δ_{ma x}$	$W, L, E, I$
Simple Beam – Concentrated Load at Centre	$R$ , $M_{ma x}$ , $Δ_{ma x}$	$P, L, E, I$
Simple Beam – Concentrated Load at Any Point	$L_{1}$ , $R_{1}$ , $R_{2}$ , $M_{ma x}$ , $Δ_{ma x}$	$P, a, b, E, I$
Simple Beam – Two Equal Concentrated Loads Symmetrically Placed	$R$ , $M_{ma x}$ , $Δ_{ma x}$	$P, L, a, E, I$
Simple Beam – Two Equal Concentrated Loads Unsymmetrically Placed	$R_{1}$ , $R_{2}$ , $M_{1}$ , $M_{2}$	$P, L, a, b$
Simple Beam – Two Unequal Concentrated Loads Unsymmetrically Placed	$R_{1}$ , $R_{2}$ , $M_{1}$ , $M_{2}$	$P_{1}, P_{2}, L, a, b$

Cantilever Beams

Case	Gives	Inputs
Cantilever Beam – Uniformly Distributed Load	$R$ , $M_{ma x}$ , $Δ_{ma x}$	$w, L, E, I$
Cantilever Beam – Concentrated Load at Free End	$R$ , $M_{ma x}$ , $Δ_{ma x}$	$P, L, E, I$
Cantilever Beam – Concentrated Load at Any Point	$R$ , $M_{ma x}$ , $Δ_{ma x}$	$P, L, b, E, I$

Propped Cantilevers

Case	Gives	Inputs
Beam Fixed at One End, Supported at Other – Uniformly Distributed Load	$R_{1}$ , $R_{2}$ , $M_{ma x}$ , $M$ , $Δ_{ma x}$	$w, L, E, I$
Beam Fixed at One End, Supported at Other – Concentrated Load at Centre	$R_{1}$ , $R_{2}$ , $M_{ma x}$ , $M$ , $x$ , $Δ_{ma x}$	$P, L, E, I$
Beam Fixed at One End, Supported at Other – Concentrated Load at Any Point	$L_{1}$ , $R_{1}$ , $R_{2}$ , $M_{1}$ , $M_{2}$	$P, a, b$

Overhanging Beams

Case	Gives	Inputs
Beam Overhanging One Support – Uniformly Distributed Load	$R_{1}$ , $R_{2}$ , $V_{ma x}$ , $x$ , $M_{1}$ , $M_{2}$	$w, L, a$
Beam Overhanging One Support – Uniformly Distributed Load on Overhang	$R_{1}$ , $R_{2}$ , $V_{ma x}$ , $M_{ma x}$ , $Δ_{ma x}$	$w, L, a, E, I$
Beam Overhanging One Support – Concentrated Load at End of Overhang	$R_{1}$ , $R_{2}$ , $V_{ma x}$ , $M_{ma x}$ , $Δ$ , $Δ_{2}$	$P, L, a, E, I$
Beam Overhanging One Support – Concentrated Load at Any Point Between Supports	$L_{1}$ , $R_{1}$ , $R_{2}$ , $M_{ma x}$	$P, a, b$
Beam Overhanging Both Supports – Unequal Overhangs – Uniformly Distributed Load	$L_{1}$ , $R_{1}$ , $R_{2}$ , $M_{1}$ , $M_{2}$ , $X$ , $M_{3}$ , $V_{ma x}$	$w, a, b, c$

Fixed-End Beams

Case	Gives	Inputs
Beam Fixed at Both Ends – Uniformly Distributed Load	$R$ , $M_{ma x}$ , $M$ , $Δ_{ma x}$	$w, L, E, I$
Beam Fixed at Both Ends – Concentrated Load at Centre	$R$ , $M_{ma x}$ , $Δ_{ma x}$	$P, L, E, I$
Beam Fixed at Both Ends – Concentrated Load at Any Point	$L_{1}$ , $R_{1}$ , $R_{2}$ , $M_{1}$ , $M_{2}$ , $M_{a}$ , $Δ_{ma x}$ , $Δ_{a}$	$P, a, b, E, I$

Continuous Beams

Case	Gives	Inputs
Continuous Beam – Two Equal Spans – Uniform Load on One Span	$R_{1}$ , $R_{2}$ , $R_{3}$ , $V_{ma x}$ , $M_{ma x}$ , $x$ , $M$	$w, L$
Continuous Beam – Two Equal Spans – Concentrated Load at Centre of One Span	$R_{1}$ , $R_{2}$ , $R_{3}$ , $V_{ma x}$ , $M_{ma x}$ , $M$	$P, L$
Continuous Beam – Two Equal Spans – Concentrated Load at Any Point	$L_{1}$ , $R_{1}$ , $R_{2}$ , $R_{3}$ , $M_{1}$ , $M_{2}$	$P, a, b$
Continuous Beam – Two Equal Spans – Uniformly Distributed Load	$R_{1}$ , $R_{2}$ , $V_{ma x}$ , $M_{ma x}$ , $M_{s p an}$ , $Δ_{ma x}$	$w, L, E, I$
Continuous Beam – Two Equal Spans – Two Equal Concentrated Loads Symmetrically Placed	$R_{1}$ , $R_{2}$ , $V_{ma x}$ , $M_{1}$ , $M_{2}$	$P, L$
Continuous Beam – Two Unequal Spans – Uniformly Distributed Load	$M$ , $R_{1}$ , $R_{3}$ , $R_{2}$ , $V_{2}$ , $V_{3}$ , $M_{x 1}$ , $M_{x 2}$	$w, L_{1}, L_{2}$
Continuous Beam – Two Unequal Spans – Concentrated Load on Each Span Symmetrically Placed	$M$ , $R_{1}$ , $R_{3}$ , $R_{2}$ , $V_{2}$ , $V_{3}$ , $M_{m 1}$ , $M_{m 2}$	$P_{1}, P_{2}, L_{1}, L_{2}$