Beam check

Works like MATLAB or a Jupyter notebook. Check a workshop gantry beam under a hoist: reactions, bending moment, stress, safety factor and deflection.

Structures desk

Basin Ridge EngineeringNot checked yet

QuickCruit Compute

Current folder

/projects/beam_calcs

beam_calcs
beam_calcs.qclive

Type: Live script
Cells: 4
Last run: Not yet

Workspace

Name	Value	Unit

Run the script to fill the workspace.

beam_calcs.qclive

How this notebook works
Write a number with its unit straight after it: 1.62 kg, 66 mm, 9.81 m/s^2. The notebook checks units as it goes and converts for you, so v to km/h shows a speed in km/h, and adding metres to seconds stops with a message.
Lists look like [0, 0.1, 0.25] s, ranges like 0:0.01:2, and positions count from 1, so x[1] is the first value. A one-line function reads area(d) = pi * d^2 / 4. Loops read for k in 1:10 or while v >= 0 m/s, and close with end.
Ctrl or Cmd + Enter runs every cell, top to bottom, with shared variables.
[1]
```
# Gantry beam, simply supported: pin at A (x = 0), roller at B (x = L)
L = 2.7 m
P = 10 kN     # hoist load, hung at x = a
a = 0.9 m
w = 1.2 kN/m  # rail and fittings, spread over the whole span

# Section: solid rectangle, width b, depth h (the load acts along h)
b = 60 mm
h = 125 mm

# Material: aluminium 6061-T6
sy = 276 MPa  # yield strength
E = 69 GPa
 
```
# Gantry beam, simply supported: pin at A (x = 0), roller at B (x = L) L = 2.7 m P = 10 kN # hoist load, hung at x = a a = 0.9 m w = 1.2 kN/m # rail and fittings, spread over the whole span # Section: solid rectangle, width b, depth h (the load acts along h) b = 60 mm h = 125 mm # Material: aluminium 6061-T6 sy = 276 MPa # yield strength E = 69 GPaTab indents. To move focus out of the cell, press Escape, then Tab.
Your answers
Store each in the name the task asks for: R_A, R_B, M_max, sigma_max, SF and d_mid, and plot both diagrams. Add as many cells as you like.
[2]
```
# Your work starts here

 
```
# Your work starts here Tab indents. To move focus out of the cell, press Escape, then Tab.

Command window

Run the script, or type a command after the prompt. It sees the script's variables.

Not run yet

SI units

The 10 kN hoist goes on the workshop gantry this week, hung 0.9 m from the A end of the 2.7 m span, with 1.2 kN/m of rail and fittings along the whole beam. Nobody lifts with it until the beam is checked. Section and material are in the first code cell.

Treat it as simply supported, pin at A and roller at B. What I need back:

the reactions at A and B
the shear and moment diagrams, since the hoist isn't at midspan and I want to see where the moment peaks
the peak bending stress and the safety factor against yield
how far the middle sags

Keep the names from the notes. The numbers go straight onto the sign-off sheet.

Basin Ridge Engineering is a made-up company. A practice scenario, built for you.

Support reactions at A and B in R_A and R_B (N)
Plot the shear V and bending moment M along the beam, and store the largest moment in M_max (N·m)
The largest bending stress, sigma = M c / I, in sigma_max (Pa)
The safety factor against yield, in SF (a plain number)
Deflection at midspan from both loads, in d_mid (m)

Checking runs the whole notebook first, then reads your named answers. Write units in and the notebook keeps them straight.

# Gantry beam, simply supported: pin at A (x = 0), roller at B (x = L) L = 2.7 m P = 10 kN # hoist load, hung at x = a a = 0.9 m w = 1.2 kN/m # rail and fittings, spread over the whole span # Section: solid rectangle, width b, depth h (the load acts along h) b = 60 mm h = 125 mm # Material: aluminium 6061-T6 sy = 276 MPa # yield strength E = 69 GPa

Beam check

How this notebook works

Your answers

How this notebook works

Your answers