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Combinded Stresses For W-Sections

Input - Torsion

Length of beam (used in torsion calcs)

L.t 10 ft * :

Torsion - uniformly distributed or max value if varying

M.t 2.68 kip * in ft / * :

Material Properties

F.y 50 ksi * :

Yield strength

Modulus of Elasticity

E 29000 ksi * :

Shear Modulus of Elasticity

G 11200 ksi * :

Section Properties - General

Depth of W-section

d 8 in * :

Web thickness

t.w 0.285 in * :

Flange width

b.f 6.54 in * :

Flange thickness

t.f 0.465 in * :

S.x 24.3 in 3^* :

Section Modulus

Torsional Constant

J 0.537 in 4^* :

Warping Constant

C.w 312 in 6^* :

Note: C.w = (I.y*h^2) / 4

Effective web height

h d t.f - :

h in 7.535

Section Properties - Torsion

Normalized warping function

W.n0 h b.f * 4 / :

W.n0 in 2^12.3197

S.w W.n0 b.f * t.f * 4 / :

Warping statical moment

S.w in 4^9.3664

Q.f h t.f * b.f t.w - (* 4 / :

Q.f in 3^5.479

First moment of area of flange

Q.w h b.f * t.f * 2 / h t.f - (2^t.w * 8 / + :

Q.w in 3^13.2381

First moment of area of web

(Note: W.ns and S.ws vary around the section but the values given in DG9 are given for worst case)

Normalized warping function at point S on section

W.ns W.n0 :

W.ns in 2^12.3197

Warping statical moment at point S on a section

S.ws S.w :

S.ws in 4^9.3664

Torsional Constant

J in 4^0.537

Warping Constant

C.w in 6^312

Note: C.w = (I.y*h^2) / 4

a E C.w * G J * / sqrt :

a in 38.7865

Torsion of W-Section for uniform torsion with pinned ends (CASE 4)

θ.4 M.t a 2^* G J * / L.t 2^2 a 2^* / z L.t / z 2^L.t 2^/ - (* z a / cosh + L.t 2 a * / tanh z a / sinh * - 1.0 - (* :

d' θ.4 (z diff : 70308713433310572159710827413700 m 2^* 1381274971061526227 sqrt * 250266879187671413 sqrt * / tanh z 274971061526227 sqrt * m 266879187671413 sqrt * / sinh * + z 274971061526227 sqrt * m 266879187671413 sqrt * / cosh - (* 297390477822785 z * 381 m * 125 z * - (* - (* 908201912104870000000000000000000 m 2^* / - z diff

d'' d' (z diff : 70308713433310572159710827413700 m 2^* 1381274971061526227 sqrt * 250266879187671413 sqrt * / tanh z 274971061526227 sqrt * m 266879187671413 sqrt * / sinh * + z 274971061526227 sqrt * m 266879187671413 sqrt * / cosh - (* 297390477822785 z * 381 m * 125 z * - (* - (* 908201912104870000000000000000000 m 2^* / - z diff z diff

d''' d'' (z diff : 70308713433310572159710827413700 m 2^* 1381274971061526227 sqrt * 250266879187671413 sqrt * / tanh z 274971061526227 sqrt * m 266879187671413 sqrt * / sinh * + z 274971061526227 sqrt * m 266879187671413 sqrt * / cosh - (* 297390477822785 z * 381 m * 125 z * - (* - (* 908201912104870000000000000000000 m 2^* / - z diff z diff z diff

Warping Stress

Point of Eval 1

Point of evaluation for torsion

z L.t 2 / :

z ft 5

Warping stress at point of evaluation

σ.ws E W.ns * d'' * abs :

σ.ws ksi #

θ.4 deg 1.9327

Rotation

θ.4 rad 0.0337

Point of Eval 2

Point 2 of evaluation for torsion

z 0 ft * :

z ft 0

Warping stress at point of evaluation

σ.ws E W.ns * d'' * abs :

σ.ws ksi #

Shear Stress - Web

Shear due to pure torsion

τ.tw G t.w * d' * :

τ.tw ksi #

Shear due to warping

τ.wsw E S.ws * d''' * t.w / - :

τ.wsw ksi #

Shear Stress - Flange

Shear due to pure torsion

τ.tf G t.f * d' * :

τ.tf ksi #

Shear due to warping

τ.wsf E S.ws * d''' * t.f / - :

τ.wsf ksi #

Rotation

θ.4 rad 0

WHEN COMBINING STRESSES - CHECK TOTAL NORMAL STRESS VS ALLOWABLE FOR YEILDING THEN CHECK UNIT OF ALLOWABLE RATIOS MX - YIELD, LOCAL AND LTB | MY - YIELD | WARPING - YIELD