Frame Analysis Calculators - Engineering Tools

1. Clear-Span-Frame: Central Vertical Point Load (Pinned-Roller Frame)

Column height (h), m

Beam span length (L), m

Concentrated load magnitude (P), kN

Modulus of elasticity (E), MPa

Moment of inertia (I), m^4

Clear-Span-Frame with Central Vertical Load

📐 Support Reactions & Results

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

M_max (Maximum moment at point 1): - kN⋅m

δ_Dh (Horizontal displacement at point D): - mm

📐 Mathematical Formulas

R_a = R_d = P/2

Left and right support vertical reactions

H_a = 0 kN

Left support horizontal reaction

M_max = P·L/4

Maximum moment at point 1

δ_Dh = P·h·L²/(8·E·I) [mm]

Horizontal displacement at point D

2. Clear-Span-Frame: Top Side Horizontal Point Load (Pinned-Roller Frame)

Column height (h), m

Beam span length (L), m

Concentrated load magnitude (P), kN

Modulus of elasticity (E), MPa

Moment of inertia (I), m^4

Clear-Span-Frame with Top Side Horizontal Load

📐 Support Reactions & Results

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_max (Maximum moment): - kN⋅m

δ_Ch (Horizontal displacement at point C): - mm

δ_Dh (Horizontal displacement at point D): - mm

📐 Mathematical Formulas

R_a = R_d = P·h/L

Left and right support vertical reactions

H_a = P

Left support horizontal reaction

M_max = P·h

Maximum moment at point B

δ_Ch = P·h²·(L + h)/(3·E·I) [mm]

Horizontal displacement at point C

δ_Dh = P·h²·(3·L + 2·h)/(6·E·I) [mm]

Horizontal displacement at point D

3. Clear-Span-Frame: Bottom Side Horizontal Point Load (Pinned-Roller Frame)

Column height (h), m

Beam span length (L), m

Concentrated load magnitude (P), kN

Modulus of elasticity (E), MPa

Moment of inertia (I), m^4

Clear-Span-Frame with Bottom Side Horizontal Load

📐 Support Reactions & Results

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

M_max (Maximum moment): - kN⋅m

δ_Dh (Horizontal displacement at point D): - mm

📐 Mathematical Formulas

R_a = R_d = 0 kN

Left and right support vertical reactions

H_a = P

Left support horizontal reaction

M_max = P·h

Maximum moment at points B & C

δ_Dh = P·h²·(3·L + 2·h)/(3·E·I) [mm]

Horizontal displacement at point D

4. Clear-Span-Frame: (Pinned-Roller) - Top Side Concentrated Moment

Column height (h), m

Beam span length (L), m

Concentrated moment magnitude (M), kN⋅m

Modulus of elasticity (E), MPa

Moment of inertia (I), m^4

Clear-Span-Frame with Top Side Concentrated Moment

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

M_max (Maximum moment at points C): - kN⋅m

δ_Dh (Horizontal displacement at point D): - mm

📐 Mathematical Formulas

R_a = R_d = M/L

Left and right support vertical reactions

H_a = 0 kN

Left support horizontal reaction

M_max = M

Maximum moment at point C

δ_Dh = M·h·L/(2·E·I) [mm]

Horizontal displacement at point D

5. Clear-Span-Frame: (Pinned-Roller) - Central Concentrated Moment on Beam

Column height (h), m

Beam span length (L), m

Concentrated moment magnitude (M), kN⋅m

Modulus of elasticity (E), MPa

Moment of inertia (I), m^4

Clear-Span-Frame with Central Concentrated Moment

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

M_max (Maximum moment at points 1): - kN⋅m

θ_1 (Slope at point 1): - rad

📐 Mathematical Formulas

R_a = R_d = M/L

Left and right support vertical reactions

H_a = 0 kN

Left support horizontal reaction

M_max = M/2

Maximum moment at point 1

θ₁ = M·L/(12·E·I)

Slope at point 1

6. Clear-Span-Frame: Vertical Uniform Load on Beam (Pinned-Roller Frame)

Column height (h), m

Beam span length (L), m

Uniform load intensity (u), kN/m

Modulus of elasticity (E), MPa

Moment of inertia (I), m^4

Clear-Span-Frame with Vertical Uniform Load on Beam

📐 Support Reactions & Results

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

M_max (Maximum moment at point 1): - kN⋅m

δ_Dh (Horizontal displacement at point D): - mm

📐 Mathematical Formulas

R_a = R_d = u·L/2

Left and right support vertical reactions

H_a = 0 kN

Left support horizontal reaction

M_max = u·L²/8

Maximum moment at point 1

δ_Dh = u·h·L³/(12·E·I) [mm]

Horizontal displacement at point D

7. Clear-Span-Frame: (Pinned-Roller) - Left Column Horizontal Uniform Load

Column height (h), m

Beam span length (L), m

Uniform load intensity (u), kN/m

Modulus of elasticity (E), MPa

Moment of inertia (I), m^4

Clear-Span-Frame with Left Column Horizontal Uniform Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

M_max (Maximum moment at point B): - kN⋅m

δ_Dh (Horizontal displacement at point D): - mm

📐 Mathematical Formulas

R_a = R_d = u·h²/(2·L)

Left and right support vertical reactions

H_a = u·h

Left support horizontal reaction

M_max = u·h²/2

Maximum moment at point B

δ_Dh = u·h³·(6·L + 5·h)/(24·E·I) [mm]

Horizontal displacement at point D

8. Clear-Span-Frame: (Pinned-Roller) - Right Column Horizontal Uniform Load

Column height (h), m

Beam span length (L), m

Uniform load intensity (u), kN/m

Modulus of elasticity (E), MPa

Moment of inertia (I), m^4

Clear-Span-Frame with Right Column Horizontal Uniform Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

M_C (Moment at point C): - kN⋅m

M_max (Maximum moment at point B): - kN⋅m

δ_Dh (Horizontal displacement at point D): - mm

📐 Mathematical Formulas

R_a = R_d = u·h²/(2·L)

Left and right support vertical reactions

H_a = u·h

Left support horizontal reaction

M_C = u·h²/2

Moment at point C

M_max = u·h²

Maximum moment at point B

δ_Dh = u·h³·(18·L + 11·h)/(24·E·I) [mm]

Horizontal displacement at point D

9. Clear-Span-Frame: (Pinned-Pinned) - Central Vertical Point Load on Beam

Column height (h), m

Beam span length (L), m

Location of point load from left support (x), m

Concentrated load magnitude (P), kN

Modulus of elasticity (E), MPa

Beam section moment of inertia (I_b), m^4

Column section moment of inertia (I_c), m^4

Clear-Span-Frame (Pinned-Pinned) with Central Vertical Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_b (Moment at point B): - kN⋅m

M_c (Moment at point C): - kN⋅m

M_1 (Moment at point 1): - kN⋅m

📐 Mathematical Formulas

ε = h/L

Geometric ratio

μ = I_b/I_c

Moment of inertia ratio

R_a = P·(L - x)/L

Left support vertical reaction

R_d = P·x/L

Right support vertical reaction

H_a = H_d = 3·P·x·(L - x)/(2·h·L·(2·μ·ε + 3))

Horizontal reactions

M_b = M_c = 3·P·x·(L - x)/(2·L·(2·μ·ε + 3))

Moments at B and C

M₁ = P·x·(L - x)·(4·μ·ε + 3)/(2·L·(2·μ·ε + 3))

Moment at midspan (point 1)

10. Clear-Span-Frame: (Pinned-Pinned) - Top Side Horizontal Point Load

Column height (h), m

Beam span length (L), m

Concentrated load magnitude (P), kN

Modulus of elasticity (E), MPa

Beam section moment of inertia (I_b), m^4

Column section moment of inertia (I_c), m^4

Clear-Span-Frame (Pinned-Pinned) with Top Side Horizontal Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_b (Moment at point B): - kN⋅m

M_c (Moment at point C): - kN⋅m

Mathematical Formulas

ε = h/L

Geometric ratio

μ = I_b/I_c

Moment of inertia ratio

R_a = R_d = P·h/L

Left and right support vertical reactions

H_a = H_d = P/2

Horizontal reactions at supports

M_b = M_c = P·h/2

Moments at points B and C

11. Clear-Span-Frame: (Pinned-Pinned) - Side Point Load

Column height (h), m

Beam span length (L), m

Location of point load from top of left support (y), m

Concentrated load magnitude (P), kN

Modulus of elasticity (E), MPa

Beam section moment of inertia (I_b), m^4

Column section moment of inertia (I_c), m^4

Clear-Span-Frame (Pinned-Pinned) with Side Point Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_1 (Maximum moment at point 1): - kN⋅m

M_b (Moment at point B): - kN⋅m

M_c (Moment at point C): - kN⋅m

Mathematical Formulas

ε = h/L

Geometric ratio

μ = I_b/I_c

Moment of inertia ratio

R_a = R_d = P·(h - y)/L

Left and right support vertical reactions

H_a = (P/(2·h))·(h + y - (h - y)·y·μ·(2·h - y)/(h·(2·h·μ + 3·L)))

Left support horizontal reaction

H_d = (P·(h - y)/(2·h))·(1 + y·μ·(2·h - y)/(h·(2·h·μ + 3·L)))

Right support horizontal reaction

M₁ = (P·(h - y)/(2·h))·(h + y - (h - y)·y·μ·(2·h - y)/(h·(2·h·μ + 3·L)))

Maximum moment at point 1

M_b = (P·(h - y)/2)·(1 - y·μ·(2·h - y)/(h·(2·h·μ + 3·L)))

Moment at point B

M_c = (P·(h - y)/2)·(1 + y·μ·(2·h - y)/(h·(2·h·μ + 3·L)))

Moment at point C

12. Clear-Span-Frame: (Pinned-Pinned) - Vertical Uniform Load on Beam

Column height (h), m

Beam span length (L), m

Uniform load intensity (u), kN/m

Modulus of elasticity (E), MPa

Beam section moment of inertia (I_b), m^4

Column section moment of inertia (I_c), m^4

Clear-Span-Frame (Pinned-Pinned) with Vertical Uniform Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_1 (Moment at point 1): - kN⋅m

M_b (Moment at point B): - kN⋅m

M_c (Moment at point C): - kN⋅m

Mathematical Formulas

ε = h/L

Geometric ratio

μ = I_b/I_c

Moment of inertia ratio

R_a = R_d = u·L/2

Left and right support vertical reactions

H_a = H_d = u·L/(4·ε·(2·μ·ε + 3))

Horizontal reactions at supports

M₁ = u·L²·(2·μ·ε + 1)/(8·(2·μ·ε + 3))

Moment at midspan (point 1)

M_b = M_c = u·L²/(4·(2·μ·ε + 3))

Moments at points B and C

13. Clear-Span-Frame: (Pinned-Pinned) - Left Column Horizontal Uniform Load

Column height (h), m

Beam span length (L), m

Uniform load intensity (u), kN/m

Modulus of elasticity (E), MPa

Beam section moment of inertia (I_b), m^4

Column section moment of inertia (I_c), m^4

Clear-Span-Frame (Pinned-Pinned) with Left Column Horizontal Uniform Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_b (Moment at point B): - kN⋅m

M_c (Moment at point C): - kN⋅m

Mathematical Formulas

ε = h/L

Geometric ratio

μ = I_b/I_c

Moment of inertia ratio

R_a = R_d = u·h²/(2·L)

Left and right support vertical reactions

H_a = u·h·(11·μ·ε + 18)/(8·(2·μ·ε + 3))

Left support horizontal reaction

H_d = u·h·(5·μ·ε + 6)/(8·(2·μ·ε + 3))

Right support horizontal reaction

M_b = 3·u·h²·(μ·ε + 2)/(8·(2·μ·ε + 3))

Moment at point B

M_c = u·h²·(5·μ·ε + 6)/(8·(2·μ·ε + 3))

Moment at point C

14. Clear-Span-Frame: (Fixed-Fixed) - Central Vertical Point Load on Beam

Column height (h), m

Beam span length (L), m

Concentrated load magnitude (P), kN

Modulus of elasticity (E), MPa

Beam section moment of inertia (I_b), m^4

Column section moment of inertia (I_c), m^4

Clear-Span-Frame (Fixed-Fixed) with Central Vertical Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_a (Moment at point A): - kN⋅m

M_b (Moment at point B & C): - kN⋅m

M_c (Moment at point C): - kN⋅m

M_d (Moment at point D): - kN⋅m

M_1 (Moment at point 1): - kN⋅m

Mathematical Formulas

ε = h/L

Geometric ratio

μ = I_b/I_c

Moment of inertia ratio

R_a = R_d = P/2

Left and right support vertical reactions

H_a = H_d = 3·P·L/(8·h·(μ·ε + 2))

Horizontal reactions at supports

M_a = M_d = P·L/(8·(μ·ε + 2))

Moments at supports A and D

M_b = M_c = P·L/(4·(μ·ε + 2))

Moments at points B and C

M₁ = (P·L/8)·((μ·ε + 1)/(μ·ε + 2))

Moment at midspan (point 1)

15. Clear-Span-Frame: (Fixed-Fixed) - Vertical Uniform Load on Beam

Column height (h), m

Beam span length (L), m

Uniform load intensity (u), kN/m

Modulus of elasticity (E), MPa

Beam section moment of inertia (I_b), m^4

Column section moment of inertia (I_c), m^4

Clear-Span-Frame (Fixed-Fixed) with Vertical Uniform Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_a (Moment at point A): - kN⋅m

M_b (Moment at point B): - kN⋅m

M_c (Moment at point C): - kN⋅m

M_d (Moment at point D): - kN⋅m

M_1 (Moment at point 1): - kN⋅m

Mathematical Formulas

ε = h/L

Geometric ratio

μ = I_b/I_c

Moment of inertia ratio

R_a = R_d = u·L/2

Left and right support vertical reactions

H_a = H_d = u·L²/(4·h·(μ·ε + 2))

Horizontal reactions at supports

M_a = M_d = u·L²/(12·(μ·ε + 2))

Moments at supports A and D

M_b = M_c = u·L²/(6·(μ·ε + 2))

Moments at points B and C

M₁ = (u·L²/24)·((3·μ·ε + 1)/(μ·ε + 2))

Moment at midspan (point 1)

16. Clear-Span-Frame: (Fixed-Fixed) - Left Column Horizontal Uniform Load

Column height (h), m

Beam span length (L), m

Uniform load intensity (u), kN/m

Modulus of elasticity (E), MPa

Beam section moment of inertia (I_b), m^4

Column section moment of inertia (I_c), m^4

Clear-Span-Frame (Fixed-Fixed) with Left Column Horizontal Uniform Load

📐 Support Reactions

R_a (Left support vertical reaction): - kN

R_d (Right support vertical reaction): - kN

H_a (Left support horizontal reaction): - kN

H_d (Right support horizontal reaction): - kN

M_a (Moment at point A): - kN⋅m

M_b (Moment at point B): - kN⋅m

M_c (Moment at point C): - kN⋅m

M_d (Moment at point D): - kN⋅m

M_1 (Moment at point 1): - kN⋅m

Mathematical Formulas

ε = h/L

Geometric ratio

μ = I_b/I_c

Moment of inertia ratio

R_a = R_d = u·h·μ·ε²/(6·μ·ε + 1)

Left and right support vertical reactions

H_a = (u·h/4)·((8·μ·ε + 17)/(2·(μ·ε + 2)) - (4·μ·ε + 3)/(6·μ·ε + 1))

Left support horizontal reaction

H_d = (u·h/4)·((4·μ·ε + 3)/(6·μ·ε + 1) - 1/(2·(μ·ε + 2)))

Right support horizontal reaction

M_a = (u·h²/4)·((4·μ·ε + 1)/(6·μ·ε + 1) + (μ·ε + 3)/(6·(μ·ε + 2)))

Moment at point A

M_b = (u·h²·μ·ε/4)·(6/(6·μ·ε + 1) - 1/(6·(μ·ε + 2)))

Moment at point B

M_c = (u·h²·μ·ε/4)·(2/(6·μ·ε + 1) - 1/(6·(μ·ε + 2)))

Moment at point C

M_d = (u·h²/4)·((4·μ·ε + 1)/(6·μ·ε + 1) - (μ·ε + 3)/(6·(μ·ε + 2)))

Moment at point D

1. Clear-Span-Frame: Central Vertical Point Load (Pinned-Roller Frame)

📐 Support Reactions & Results

📐 Mathematical Formulas

2. Clear-Span-Frame: Top Side Horizontal Point Load (Pinned-Roller Frame)

📐 Support Reactions & Results

📐 Mathematical Formulas

3. Clear-Span-Frame: Bottom Side Horizontal Point Load (Pinned-Roller Frame)

📐 Support Reactions & Results

📐 Mathematical Formulas

4. Clear-Span-Frame: (Pinned-Roller) - Top Side Concentrated Moment

📐 Support Reactions

📐 Mathematical Formulas

5. Clear-Span-Frame: (Pinned-Roller) - Central Concentrated Moment on Beam

📐 Support Reactions

📐 Mathematical Formulas

6. Clear-Span-Frame: Vertical Uniform Load on Beam (Pinned-Roller Frame)

📐 Support Reactions & Results

📐 Mathematical Formulas

7. Clear-Span-Frame: (Pinned-Roller) - Left Column Horizontal Uniform Load

📐 Support Reactions

📐 Mathematical Formulas

8. Clear-Span-Frame: (Pinned-Roller) - Right Column Horizontal Uniform Load

📐 Support Reactions

📐 Mathematical Formulas

9. Clear-Span-Frame: (Pinned-Pinned) - Central Vertical Point Load on Beam

📐 Support Reactions

📐 Mathematical Formulas

10. Clear-Span-Frame: (Pinned-Pinned) - Top Side Horizontal Point Load

📐 Support Reactions

Mathematical Formulas

11. Clear-Span-Frame: (Pinned-Pinned) - Side Point Load

📐 Support Reactions

Mathematical Formulas

12. Clear-Span-Frame: (Pinned-Pinned) - Vertical Uniform Load on Beam

📐 Support Reactions

Mathematical Formulas

13. Clear-Span-Frame: (Pinned-Pinned) - Left Column Horizontal Uniform Load

📐 Support Reactions

Mathematical Formulas

14. Clear-Span-Frame: (Fixed-Fixed) - Central Vertical Point Load on Beam

📐 Support Reactions

Mathematical Formulas

15. Clear-Span-Frame: (Fixed-Fixed) - Vertical Uniform Load on Beam

📐 Support Reactions

Mathematical Formulas

16. Clear-Span-Frame: (Fixed-Fixed) - Left Column Horizontal Uniform Load

📐 Support Reactions

Mathematical Formulas

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