Common Vertical Force and Bending Moment Diagrams - read online free

Oct 25, 2026

RAIC Centre for Architecture at Athabasca University presents common beam load cases with corresponding free body diagram, vertical force (shear) diagram, and bending moment diagram. The guide covers multiple beam types including simply supported beams with concentrated and distributed loading, fixed at both ends, and cantilevers. For each case, connectors, reactions, shear/vertical force relationships, and key bending moment expressions at critical locations are listed to support accurate structural analysis.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages1

Reading Time3 min

AccessFree to download

Beam type overview

Free body diagram, vertical force (V), and bending moment (M)

Load types and supports

Reactions, key V expressions, and key M locations

RAIC Centre for Architecture at Athabasca University Common Vertical Force and Bending Moment Diagrams | Beam Type | Simple | | | Simple | | Simple | Simple | | | Simple | | Fixed at Both Ends | Fixed at Both Ends | | Cantilever | Cantilever | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Free Body Diagram
Vertical Force (V) or Shear Diagram
Bending Moment (M) Diagram |
| | |

| |
R1 R2
V1 |
| | |

R1
V1
Mmax | |

Ma M2
R1
V1
V2
M1 |

M1 Mmax

Mmax
V
V | |

Mmax |

Mmax | | Load | Concentrated Load at Centre | | | Concentrated Load at Any Point | | 2 Unequal Concentrated Loads Unsymmetrically Placed | Uniformly
Distributed Load | | | Load Increasing Uniformly Towards One End | | Concentrated Load at any Point | Uniformly
Distributed Loads | | Concentrated Load at any Point | Uniformly
Distributed Loads | | Connectors | Pin and Roller | | | Pin and Roller | | Pin and Roller | Pin and Roller | | | Pin and Roller | | Fixed | Fixed | | Cantilever | Cantilever | | Reactions | 􀀡 = 􀀣 | | | 􀀡 $ = 􀀣$
􀀡 % = 􀀣% | | 􀀡 $ = 􀀣$
􀀡 % = 􀀣% | 􀀡 = 􀀣 | | | 􀀡 $ = 􀀣$
􀀡 % = 􀀣% | | 􀀡 $ = 􀀣$
􀀡 % = 􀀣% | 􀀡 = 􀀣 | | 􀀡 = 􀀣 | 􀀡 = 􀀣 | | Vertical Force | 􀀣 = | 􀀦 2 | | 􀀣$ =
􀀣% = | 􀀦􀀨􀀩􀀦􀀪􀀩 | 􀀣$ = 􀀦$ (􀀩 − 􀀪) + 􀀦% 􀀨􀀩
􀀣% = 􀀦%(􀀩~~ ~~−~~ ~~􀀨􀀩)~~ ~~+~~ ~~􀀦$~~ ~~􀀪 | 􀀣 = | 􀀯􀀩 2 | | 􀀣$ =
􀀰 3
􀀣% =
2􀀰
3
􀀯ℎ􀀳􀀴􀀳 􀀰 = | 􀀯􀀩 2 | 􀀦􀀨 %(3􀀪 + 􀀨)􀀣$ = 􀀩 6
􀀦 􀀪 %(3􀀨 + 􀀪)􀀣% = 􀀩 6 | 􀀣 = | 􀀯􀀩 2 | 􀀣 = 􀀦 | 􀀣 = 􀀯􀀩
􀀣7 = 􀀯􀀸 | | Bending
Moment | 􀀹:;7 = | | 􀀦􀀩 4 | 􀀹:;7 =
􀀦􀀪􀀨
􀀩
(at point of load) | | 􀀹$ = 􀀡 $ 􀀪(max. if R1>P1)
􀀹% = 􀀡 % 􀀨(max. if R2>P2) | 􀀹:;7 = | | 􀀯 􀀩 %
8 | 􀀹:;7 =

= . 1283􀀰􀀩 | | 􀀹$ =
􀀦􀀪􀀨 %
􀀩 %
(max. if a􀀹% =
􀀦􀀨 􀀪 %
􀀩 %
(max. if a>b)
􀀹; =
2􀀦􀀨 % 􀀪 %
􀀩 6
(at point of load) | 􀀹:;7 =
􀀯 􀀩 %
12
(at ends)
􀀹$ =
􀀯 􀀩 %
24
(at centre) | | 􀀹:;7 = 􀀦􀀨(at fixed end)
􀀹7 = 􀀦 (􀀸 − 􀀪)(when x>a) | 􀀹:;7 =
􀀯 􀀩 %
2
(at fixed end)
􀀹7 =
􀀯􀀸%
2 | | | (at point of load) | | | | | | | | | | | | | | | | | | | | | | | | (at centre) | | | | | | | | | |

FAQs

Which beam types are covered in the diagrams?

The material covers simply supported beams under several loading conditions, beams fixed at both ends, and cantilevers. Each beam type has associated vertical force and bending moment diagram results.

What diagrams are provided for each load case?

For each case, the guide pairs a free body diagram with the vertical force (shear) diagram and the bending moment (M) diagram. It also lists reactions and the governing expressions at key points.

Where are the maximum or critical bending moments identified?

The document specifies bending moment evaluation at critical locations such as points of load, ends, centres, and fixed ends depending on the beam type and load placement. It notes conditional maxima based on relative reaction/load magnitudes and geometry parameters.

Oct 25, 2026

Uploaded by Aria Callaghan