How to use the SFD & BMD Calculator
- 1. Pick the beamSimply supported (move the supports for an overhang) or cantilever, and its length.
- 2. Type the loadsOne per line: P 20 2 is 20 kN at 2 m, U 10 0 6 is 10 kN/m from 0 to 6 m.
- 3. Read the diagramsSee reactions, the zero-shear point, max moment and contraflexure points.
How shear force and bending moment are found
First find the reactions from equilibrium: ΣFy = 0 and ΣM = 0. For a simply supported beam, take moments about A to get RB, then RA = ΣW − RB. For a cantilever, the fixed end carries the whole load and a fixing moment.
The shear force at a section is the sum of vertical forces on the left of it (upward positive). The bending moment is the sum of moments of those forces about the section, with sagging taken as positive. The moment is largest where the shear force is zero or changes sign.
Worked example
A 6 m simply supported beam carries 20 kN at 2 m and a UDL of 10 kN/m over the full span. Total load = 20 + 60 = 80 kN. Moments about A: RB × 6 = 20 × 2 + 60 × 3 = 220, so RB = 36.67 kN and RA = 43.33 kN.
Shear just right of the point load = 43.33 − 20 − 10 × 2 = 3.33 kN, so it becomes zero 0.333 m later, at x = 2.333 m. The maximum moment there is 43.33 × 2.333 − 20 × 0.333 − 10 × 2.333² / 2 = 67.22 kN·m.
Exam tips
- Under a UDL the SFD is a straight sloping line and the BMD a parabola. Under a uniformly varying load they are a parabola and a cubic.
- A point load makes a vertical jump in the SFD. A couple makes a jump in the BMD.
- Write the moment equation for each segment and check that M = 0 at a free end or a simple support.
- Overhangs give hogging moments over the support and a point of contraflexure.
Next, find how much the beam bends with the beam deflection calculator.
Frequently asked questions
Which sign convention does the tool use?
Downward loads and clockwise couples are positive. Shear is the sum of upward forces on the left of the section, and sagging moment is positive.
Can it solve an overhanging beam?
Yes. Choose simply supported and move support A or B inwards from the beam ends. The tool shows the hogging moment and any point of contraflexure.
How do I enter a triangular load?
Use V w1 w2 from to. For example, V 0 12 0 6 is a load rising from 0 to 12 kN/m over the first 6 m.
Is this calculator free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form. Everything is calculated in your browser.