Structural calculation examples, written with units

How everyday structural calculations look in Equation Pad: a steel beam, a concrete column, a strip footing, a cantilever retaining wall, wind pressure, a timber joist, a one-way slab and bolted and welded connections. Each line below is typed exactly as shown.

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A structural calculation sheet with title block and typeset equations.

Before you start

These are short illustrations of how a calculation is written in Equation Pad, with simplified textbook formulas. They are not a design method: use the design code, factors and checks that apply to your work, and have the result checked by a competent engineer.

Type a line, press Enter and the next line goes below it. := defines a value, = at the end shows the result, and a unit after the = converts it. A comparison such as M_Ed <= M_Rd = shows TRUE or FALSE.

Steel beam design pad: simply supported beam with a uniform load

w := 12 kN/m
L := 6 m
M_Ed := w*L^2/8 = kN*m
V_Ed := w*L/2 = kN
W_pl := 900 cm^3
f_y := 355 MPa
M_Rd := W_pl*f_y = kN*m
M_Ed <= M_Rd =
E := 210 GPa
I := 14100 cm^4
delta := 5*w*L^4/(384*E*I) = mm
delta <= L/360 =

Concrete column design sheet: squash load of a short column

N_Ed := 1500 kN
b := 300 mm
h := 300 mm
f_ck := 30 MPa
f_yk := 500 MPa
A_s := 4*pi*(20 mm)^2/4 = mm^2
N_Rd := 0.567*f_ck*(b*h - A_s) + 0.87*f_yk*A_s = kN
N_Ed <= N_Rd =

Strip footing calculation sheet: bearing pressure

N := 180 kN/m
B := 1.2 m
g_f := 24 kN/m^3*0.5 m*B = kN/m
q := (N + g_f)/B = kPa
q_allow := 200 kPa
q <= q_allow =

Cantilever retaining wall: active pressure and overturning

gamma := 18 kN/m^3
H := 3 m
phi := 30 deg
K_a := (1 - sin(phi))/(1 + sin(phi)) =
P_a := 0.5*K_a*gamma*H^2 = kN/m
M_o := P_a*H/3 = kN
M_r := 95 kN
FoS := M_r/M_o =
FoS >= 2 =

Wind pressure calculation tool: peak pressure on a wall

rho := 1.25 kg/m^3
v_b := 22 m/s
q_b := 0.5*rho*v_b^2 = kPa
c_e := 2.1
c_pe := 0.8
w_e := q_b*c_e*c_pe = kPa

Timber beam calculation sheet: floor joist in bending

b := 47 mm
h := 200 mm
s_j := 400 mm
L := 3.6 m
w := 2.2 kPa*s_j = kN/m
M := w*L^2/8 = kN*m
W := b*h^2/6 = cm^3
sigma := M/W = MPa
f_m := 16 MPa
sigma <= f_m =

Structural slab design sheet: one-way slab moment per metre width

g_k := 6 kPa
q_k := 3 kPa
n := 1.35*g_k + 1.5*q_k = kPa
L := 4.5 m
m_Ed := n*L^2/8 = kN*m/m

Bolt connection and weld connection

F_v := 25 kN
A_s := 157 mm^2
f_ub := 800 MPa
F_vRd := 0.6*f_ub*A_s/1.25 = kN
F_v <= F_vRd =
a := 6 mm
L_w := 150 mm
f_vw := 230 MPa
F_wRd := f_vw*a*L_w = kN

Continuous beams, trusses, base plates and frames

For continuous beams, trusses, portal and gable frames, write the stiffness matrices with matrix operations and solve with lusolve, or keep the member forces from another program in a spreadsheet on the sheet and check each member below it. A program block handles repeated checks such as several load cases or every bolt in a group.

Turn it into a calculation report

Every example above sits on a calculation sheet with a title block, sign-off boxes and your logo. Add a sketch from the drawing board, then make a PDF or a .docx document: see the calculation report generator.

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Equation Pad runs in your browser, with nothing to install, and we never see or store your calculations. Results must be checked by a competent person before they are relied on; see the disclaimer.

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