| Roark's Formulas for Stress and Strain |
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| Shear, moment, slope, deflection of elastic straight beams-table 8.1 |
| W=load (N), w=unit load (N/mm), M0=applied couple (Nmm), θ0=angular displacement (rad), |
| RA and RB are the vertical end reactions at left and right respectively (N), |
| MA and MB are the reaction end moments at left and right respectively (Nmm) |
| 1a. Left end free, right end fixed (cantilever) |
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| RA (N): | RA | RB (N): | RB |
| MA (Nmm): | MA | MB (Nmm): | MB |
| σA (MPa): | σA | σB (MPa): | σB |
| θA (degrees): | θA | θB (degrees): | θB |
| deflection yA (mm): | yA | deflection yB (mm): | yB |
| Max M = MB (Nmm): | maxM | when a (mm) = | 0 |
| Max σ = σB (MPa): | max σ | ||
| Max θ = θA (degrees): | Maxθ | when a (mm) = | 0 |
| Max y = yA (mm): | maxY | when a (mm) = | 0 |
| 1b. Left end guided, right end fixed |
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| RA (N): | RA | RB (N): | RB |
| MA (Nmm): | MA | MB (Nmm): | MB |
| σA (MPa): | σA | σB (MPa): | σB |
| θA (degrees): | θA | θB (degrees): | θB |
| deflection yA (mm): | yA | deflection yB (mm): | yB |
| Max +M = MA (Nmm): | max+M | when a (mm) = | 0 |
| Max +σA (MPa): | max+σ | ||
| Max -M = MB (Nmm): | max-M | when a (mm) = | 0 |
| Max -σB (MPa): | max-σ | ||
| Max y = yA (mm): | maxY | when a (mm) = | 0 |
| 1c. Left end simply supported, right end fixed |
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| RA (N): | RA | RB (N): | RB |
| MA (Nmm): | MA | MB (Nmm): | MB |
| σA (MPa): | σA | σB (MPa): | σB |
| θA (degrees): | θA | θB (degrees): | θB |
| deflection yA (mm): | yA | deflection yB (mm): | yB |
| Max +M (Nmm): | max+M | at x (mm) = | a |
| Max +σ (MPa): | max+σ | ||
| Max +M (Nmm): | max+M | when a (mm) = | 0.366l |
| Max +σ (MPa): | max+σ | ||
| Max -M = MB (Nmm): | max-M | ||
| Max -σ (MPa): | max-σ | ||
| Max -M (Nmm): | max-M | when a (mm)= | 0.5773l |
| Max -σ (MPa): | max-σ | ||
| Max y (mm): | maxY | at x (mm) = | x |
| Max y (mm): | maxY | when a (mm) = | 0.414l |
| 1d. Left end fixed, right end fixed |
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| RA (N): | RA | RB (N): | RB |
| MA (Nmm): | MA | MB (Nmm): | MB |
| σA (MPa): | σA | σB (MPa): | σB |
| θA (degrees): | θA | θB (degrees): | θB |
| deflection yA (mm): | yA | deflection yB (mm): | yB |
| Max +M (Nmm): | max+M | at x (mm) = | a |
| Max +σ (MPa): | max+σ | ||
| Max +M (Nmm): | max+M | when a (mm) = | l/2 |
| Max +σ (MPa): | max+σ | ||
| Max -M=MA (Nmm): | max-M | if a smaller than | l/2 |
| Max -σ (MPa): | max-σ | ||
| Max -M (Nmm): | max-M | when a (mm)= | l/3 |
| Max -σ (MPa): | max-σ |
| Max y (mm): | maxY | at x (mm) = | 2al/(l+2a) | if a greater than | l/2 |
| Max y (mm): | maxY | when a (mm) = | l/2 |
| 1e. Left end simply supported, right end simply supported |
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| RA (N): | RA | RB (N): | RB |
| MA (Nmm): | MA | MB (Nmm): | MB |
| σA (MPa): | σA | σB (MPa): | σB |
| θA (degrees): | θA | θB (degrees): | θB |
| deflection yA (mm): | yA | deflection yB (mm): | yB |
| Max M (Nmm): | maxMx | at x (mm) = | a |
| Max σ (MPa): | max σx | ||
| Max M (Nmm): | maxM | when a (mm) = | l/2 |
| Max σ (MPa): | max σ |
| Max y (mm): | maxY | at x (mm)= | l-sqrt((l^2-a^2)/3) | when a less than | l/2 |
| Max y (mm): | maxY | at x (mm)= | l/2 | and when a (mm)= | l/2 |
| Max θ = θA (degrees): | maxθ | when a less than | l/2 |
| Max θ (degrees): | maxθ | when a (mm) = | 0.423l |
| 1f. Left end guided, right end simply supported |
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| RA (N): | RA | RB (N): | RB |
| MA (Nmm): | MA | MB (Nmm): | MB |
| σA (MPa): | σA | σB (MPa): | σB |
| θA (degrees): | θA | θB (degrees): | θB |
| deflection yA (mm): | yA | deflection yB (mm): | yB |
| Max M = MA(Nmm): | maxM | for x between 0 and a | |
| Max σ = σA(MPa): | max σ | ||
| Max M = MA(Nmm): | maxM | when a (mm) = | 0 |
| Max σ = σA(MPa): | max σ | ||
| Max y = yA(mm): | maxY | ||
| Max y (mm): | maxY | when a (mm)= | 0 |
| Max θ = θB (degrees): | maxθ | ||
| Max θ (degrees): | maxθ | when a (mm) = | 0 |