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Beam calculator for bending moment, bending stress, lateral force and support reactions

This online beam calculator calculates the forces and moments in the two bearings (= support reactions) and the angles of inclination of statically determined or statically indeterminate beams. In addition, the lateral force, the bending moment, the bending stress and the deflection can be determined at a desired location. The bending moment, the shear force and the deflection as a function of the length x are shown graphically in two diagrams. The calculation of the maximum bending moment, the maximum bending stress, the maximum deflection and the associated position is possible, too.

 

The bearings can be designed as a fixed bearing, a movable bearing, a fixed clamping or as a free end. As a load, a equal load or a point load or the combination of both or a triangular load (left or right) can be selected.

Calculator for Support Reactions, Lateral Force & Bending Moment of Beams


Bearing A  
Load case
Bearing B
Träger mit Einzellast

l m   Force F kN
a m   Load q kN/m
FA kN   FB kN
MA kNm   MB kNm
xM.m m   My.m  kNm
x m   My (x) kNm
  Q (x) kN


   

Additional functions: bending stresses, angles of inclination & deflection

Calculation of area moment of inertia or section modulus with respect to
y-axis           z-axis 

A
H mm
B mm
mat.
Iy *   cm4
d mm
h mm
b mm
E ** N/mm²
Wy * cm3
Bild eines I-Trägers

σx.m  N/mm2
σx (x)  N/mm2
αA  °
αB °
xf.m  m
fm mm
f (x) mm

 

* To enter these values, select under Cross section A -> Other profiles -> "Own profile".

** The modulus of elasticity is automatically entered by selecting a material and can be changed at any time; suitable valuesyou can find on wikipedia for example.

 

Note: The inclination angles in the bearings, the position of the maximum deflection and the maximum deflection itself can not be calculated yet for all combinations!

Explanation of the abbreviations

FA reaction force in bearing A in z-direction; in the x-direction there are no forces!
FB reaction force in bearing B in z-direction; in the x-direction there are no forces!
MA clamping moment in bearing A
MB clamping moment in bearing B
xM.m

position of the maximum bending moment; Attention: only one place

is calculated even if there are several equal bending moments!

My.m maximum bending moment
x

point where the bending moment, the lateral force, the

bending stress and the maximum deflection are to be calculated

My (x) bending moment at the point x
Q (x) lateral force at the point x
A cross section of the profile
mat. material
E

Young's modulus / modulus of elasticity, suitable values

you can find on wikipedia for example

Iy area moment of inertia
Wy section modulus
σx bending stress in the outer-fibre at the point x
σx.m maximum bending stress in the beam at the point xM.m
αA  inclination angle of the beam in bearing A
αB inclination angle of the beam in bearing B
xf.m position of the maximum deflection of the beam
fm maximum deflection of the beam at the point xf.m
f (x) deflection of the beam at the point x

Manual

  • The following cross sectional areas are available, whereby profiles marked by * can have a clearance hole (bore), too:
    • circle *
    • pipe / hollow circular
    • semi-circle
    • rectangle-section *
    • rectangle-pipe / hollow rectangular *
    • I/H-section (I/H-beam) *
    • U/C-section (U/C-beam) *
    • T-section (T-beam)
    • L-section (angle section), isosceles and not isosceles
    • L-section (isosceles) rotated through 45°
    • isosceles triangle
    • hexagon / six-sided figure
    • octagon / eight-sided figure

  • The loads may also be negative.
  • Any jumps in the lateral force curve can not be displayed correctly.
  • Accuracy can not be guaranteed - for corrections or additions please use my contact form!

 

Selectable combinations

The support forces of both statically determined and statically indeterminate systems can be calculated by this calculator. The following combinations are possible:

Statically determined systems

fixed bearing - point load - movable bearing
fixed bearing - point load - movable bearing
fixed bearing - equal load - movable bearing
fixed bearing - equal load - movable bearing
fixed bearing - point & equal load - movable bearing
fixed bearing - point & equal load - movable bearing
fixed bearing - delta load right - movable bearing
fixed bearing - delta load right - movable bearing
fixed bearing - delta load left - movable bearing
fixed bearing - delta load left - movable bearing
firm clamping - point load - free end
firm clamping - point load - free end
firm clamping - equal load - free end
firm clamping - equal load - free end
firm clamping - point & equal load - free end
firm clamping - point & equal load - free end
firm clamping - delta load right - free end
firm clamping - delta load right - free end
firm clamping - delta load left - free end
firm clamping - delta load left - free end

Statically indeterminate sytems

firm clamping - point load - firm clamping
firm clamping - point load - firm clamping
firm clamping - equal load - firm clamping
firm clamping - equal load - firm clamping
firm clamping - point & equal load - firm clamping
firm clamping - point & equal load - firm clamping
firm clamping - delta load right - firm clamping
firm clamping - delta load right - firm clamping
firm clamping - delta load left - firm clamping
firm clamping - delta load left - firm clamping
firm clamping - point load - movable bearing
firm clamping - point load - movable bearing
firm clamping - equal load - movable bearing
firm clamping - equal load - movable bearing
firm clamping - point & equal load - movable bearing
firm clamping - point & equal load - movable bearing
firm clamping - delta load right - movable bearing
firm clamping - delta load right - movable bearing
firm clamping - delta load left - movable bearing
firm clamping - delta load left - movable bearing

Page created on August 2019. Last change: 04 September 2019.