Beam deflection and stress are different quantities
Engineering calculators (Beta)
Match the diagram conditions, then follow the example inputs and results. Change numerical values in the calculator.
1. Match the diagram to your question
両端で支え、中央を下向きに押す梁です。固定端の梁とは分けて考えます。
Lは支点間、Fは荷重です。断面のIとZは曲げる向きの軸に合わせ、材料のEを用意します。
梁の長さ L
1,000 mm
ヤング率 E（入力例）
200 GPa
曲げ軸の I
4,166,670 mm⁴
曲げ軸の最小 Z
83,333.3 mm³
集中荷重 F
1,000 N
破線はたわみを拡大した形です。δは動く距離、σは材料の負担で、同じ量ではありません。
δmax · 最大たわみ δmax
0.025 mm
σmax · 最大曲げ応力の絶対値
3 MPa
Mmax · 最大曲げモーメントの絶対値
250 N·m
Both ends support the beam, with a downward centre load. This differs from a cantilever.
L spans between supports; F is the load. Match section I and Z to the bending axis and obtain material E.
Span L
1,000 mm
Young’s modulus E (example)
200 GPa
I about bending axis
4,166,670 mm⁴
Smaller Z about bending axis
83,333.3 mm³
Point load F
1,000 N
The dashed deflection is exaggerated. δ measures movement; σ describes stress in the material.
δmax · Maximum deflection
0.025 mm
σmax · Maximum absolute bending stress
3 MPa
Mmax · Maximum absolute bending moment
250 N·m
Blue marks inputs; orange marks outputs. These diagrams explain the fixed example below; dimensions and deformation are not drawn to physical scale.
Supports / loading: simply supported, centre point load
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2. Example inputs
Span LWhat goes here?
Use span between supports, or the cantilever length defined by the selected diagram.
1,000 mm
Young’s modulus E (example)What goes here?
E describes axial stiffness and G shear stiffness; neither is yield strength or allowable stress.
Use the actual material, temperature and direction. Table entries are comparisons, not material specifications. For isotropic elasticity, check consistency with G=E/[2(1+ν)].
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
200 GPa
I about bending axisWhat goes here?
A section geometry property relevant to bending and buckling. Obtain it about the bending axis from section properties.
4,166,670 mm⁴
Smaller Z about bending axisWhat goes here?
The geometric section modulus Z=I/c for a specified bending axis, not an empirical material factor.
Use the actual section, bending axis and extreme-fibre distance. Transfer matching-axis properties from the section calculator or use a manufacturer section table.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
83,333.3 mm³
Point load FWhat goes here?
Magnitude of a push or pull, in force units such as N, rather than mass in kg.
1,000 N
These are fixed teaching inputs. Coefficients, properties and comparison limits are not recommendations. Enter your conditions in the calculator.
3. Results for this example
Maximum deflection
0.025 mm
Maximum absolute bending stress
3 MPa
Maximum absolute bending moment
250 N·m
Deflection measures movement; stress describes material loading. The example is a simply supported beam with a centre point load. I controls deflection and Z controls bending stress.
4. Which formula is used?
δmax = FL³ / (48EI), σmax = (FL / 4) / Z
Table units are not always the units required in the formula. The calculator converts selected units to its internal base units before computing.
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Assumptions and exclusions
Uniform homogeneous linear-elastic Euler–Bernoulli beam with small deflection. Loads act downward. Upward reactions, sagging moments and downward deflection are positive. Shear deformation, self-weight, stress concentrations, buckling and fatigue are excluded. I and Z must refer to the same principal bending axis. Deflection is exaggerated in the diagram.
