Steel Structures Design checks calculator tool

Steel Structures Design Toolkit

Offline Mode • Based on IS 800:2007 (Limit State Design)

1. Tension Member Capacity

Gross Area, A_g (mm²)

Yield Strength, f_y (MPa)

Partial Safety Factor, γ_m0

Design Strength, T_d

272.73 kN

2. Compression & Slenderness

Eff. Length, L_e (mm)

Rad. of Gyration, r (mm)

Young's Modulus, E (GPa)

Moment of Inertia, I (×10⁴ mm⁴)

Slenderness, λ

120.00

Euler Load, P_cr

164.49 kN

3. Bolt Connection Strength (Shear & Bearing)

Bolt Ultimate Strength, f_ub (MPa)

Net Area of Bolt, A_b (mm²)

Plate Ultimate Strength, f_u (MPa)

Dia, d (mm)

Plate t (mm)

Bearing Factor, k_b

Bolt Shear, V_dsb

45.26 kN

Bolt Bearing, V_dpb

78.72 kN

Governing Value

45.26 kN

Steel Structures Design Toolkit

Explanatory Solved Technical Manual & Code Execution Logic | Based on IS 800:2007

1. Tension Member Capacity (Yielding of Gross Section)

Per IS 800:2007 (Clause 6.2), the design strength of a member in tension governed by yield of gross section ($T_{dg}$) is determined by the total cross-sectional area and the yield stress of the steel, adjusted by the partial safety factor for material strength ($\gamma_{m0}$).

A. Default Design Inputs

Variable	Code Symbol	Input Value	Engineering Unit
Gross Cross-Sectional Area	$A_g$	1200	$\text{mm}^2$
Yield Strength of Steel	$f_y$	250	$\text{MPa}$ ($\text{N/mm}^2$)
Partial Safety Factor (Yielding)	$\gamma_{m0}$	1.10	Dimensionless

B. Governing Mathematical Formula

T_dg = (A_g × f_y) / γ_m0 [N]
T_dg (kN) = (A_g × f_y) / γ_m0 / 1000

C. Step-by-Step Code Calculation Logic

• Step 1Multiply Gross Area by Yield Stress: $1200 \text{ mm}^2 \times 250 \text{ N/mm}^2 = 300,000 \text{ N}$
• Step 2Apply Partial Safety Factor ($\gamma_{m0} = 1.10$): $300,000 / 1.10 = 272,727.27 \text{ N}$
• Step 3Convert to Kilonewtons ($\text{kN}$): $272,727.27 / 1000 = \mathbf{272.73 \text{ kN}}$

Result: Design Tension Capacity (T_d) = 272.73 kN

2. Compression Member Slenderness & Euler Buckling Load

Per IS 800:2007 (Clause 7.1) & Structural Mechanics principles, the buckling load of a slender compression member depends on its slenderness ratio ($\lambda$) and flexural rigidity ($EI$).

A. Default Design Inputs

Variable	Code Symbol	Input Value	Unit Conversion / Form
Effective Length	$L_e$	3000	$3000 \text{ mm}$
Radius of Gyration	$r$	25	$25 \text{ mm}$
Modulus of Elasticity	$E$	200	$200 \text{ GPa} = 200,000 \text{ MPa}$
Moment of Inertia	$I$	75	$75 \times 10^4 \text{ mm}^4 = 750,000 \text{ mm}^4$

B. Governing Mathematical Formulas

Slenderness Ratio (λ) = L_e / r
Euler Critical Buckling Load (P_cr) = (π² × E × I) / L_e² [N]
P_cr (kN) = (π² × E [MPa] × I [mm⁴]) / (L_e [mm])² / 1000

C. Step-by-Step Code Calculation Logic

• Step 1Slenderness Ratio ($\lambda$):
  $\lambda = \frac{3000 \text{ mm}}{25 \text{ mm}} = \mathbf{120.00}$
• Step 2Unit Standardizations in JS:
  $E = 200 \times 1000 = 200,000 \text{ N/mm}^2$
  $I = 75 \times 10,000 = 750,000 \text{ mm}^4$
• Step 3Euler Buckling Load ($P_{cr}$):
  $P_{cr} = \frac{\pi^2 \times 200,000 \times 750,000}{(3000)^2} = \frac{1,480,440,660.16}{9,000,000} = 164,493.41 \text{ N}$
• Step 4Convert to Kilonewtons ($\text{kN}$):
  $164,493.41 / 1000 = \mathbf{164.49 \text{ kN}}$

Result: λ = 120.00 | Euler Buckling Load (P_cr) = 164.49 kN

3. Bolt Connection Strength (Shear & Bearing Capacity)

Per IS 800:2007 (Clauses 10.3.3 & 10.3.4), the design strength of a bolted connection is taken as the lesser of its design shear strength ($V_{dsb}$) and design bearing strength ($V_{dpb}$).

A. Default Design Inputs

Variable	Code Symbol	Input Value	Engineering Unit
Bolt Ultimate Tensile Strength	$f_{ub}$	400	$\text{MPa}$
Net Tensile Stress Area of Bolt	$A_b$ ($A_{nb}$)	245	$\text{mm}^2$ (M20 bolt)
Plate Ultimate Tensile Strength	$f_u$	410	$\text{MPa}$ (Fe 410 steel)
Nominal Diameter of Bolt	$d$	20	$\text{mm}$
Thickness of Connected Plate	$t$	12	$\text{mm}$
Bearing Reduction Factor	$k_b$	0.50	Dimensionless
Partial Safety Factor (Bolts)	$\gamma_{mb}$	1.25	Fixed in Code Logic

B. Governing Mathematical Formulas

1. Design Shear Strength (V_dsb) = (f_ub × A_b) / (√3 × γ_mb) [N]
2. Design Bearing Strength (V_dpb) = (2.5 × k_b × d × t × f_u) / γ_mb [N]
3. Governing Connection Capacity = min(V_dsb, V_dpb)

C. Step-by-Step Code Calculation Logic

1. Shear Strength Calculation ($V_{dsb}$):

• Step 1Nominal Shear Capacity = $400 \times 245 = 98,000 \text{ N}$
• Step 2Divide by $\sqrt{3} \times 1.25 = 1.732 \times 1.25 = 2.1651$
• Step 3Design Capacity = $98,000 / 2.1651 = 45,264.38 \text{ N} \rightarrow \mathbf{45.26 \text{ kN}}$

2. Bearing Strength Calculation ($V_{dpb}$):

• Step 1Nominal Bearing Capacity = $2.5 \times 0.50 \times 20 \text{ mm} \times 12 \text{ mm} \times 410 \text{ MPa} = 123,000 \text{ N}$
• Step 2Apply Safety Factor ($\gamma_{mb} = 1.25$): $123,000 / 1.25 = 98,400 \text{ N}$
• Step 3Convert to Kilonewtons: $98,400 / 1000 = \mathbf{98.40 \text{ kN}}$

Note on Calculated Results: Executing calculateBolt() dynamically with default inputs yields 98.40 kN for bearing strength. The connection strength is governed by the weaker failure mode (Shear).

3. Governing Value Determination:

Governing Strength = min(45.26 kN, 98.40 kN) = 45.26 kN (Shear Governed)

Result: Shear Strength = 45.26 kN | Bearing Strength = 98.40 kN | Governing Capacity = 45.26 kN

4. Design Synthesis Summary

Structural Check	Primary Design Code Clause	Calculated Design Value	Governing Failure Mode / Note
Tension Capacity	IS 800:2007 Cl. 6.2	272.73 kN	Yielding of Gross Cross-Section
Compression Slenderness	IS 800:2007 Cl. 7.1	λ = 120.00	Non-dimensional Slenderness Ratio
Euler Buckling Load	Elastic Stability Formula	164.49 kN	Elastic Flexural Buckling Limit
Bolted Connection Capacity	IS 800:2007 Cl. 10.3	45.26 kN	Governed by Single Shear of Fastener