Question

The internal shear force at a certain section of a steel beam is V = 210 kN . The beam cross section shown in the figure has dimensions of t f = 17 mm , b f = 290 mm , d = 406 mm , and t w = 10 mm . Determine:

(a) the shear stress at point A, which is located at y A = 78 mm below the centroid of the wide-flange shape.

(b) the maximum horizontal shear stress in the wide-flange shape.     

Below, enter the magnitudes of the shear stresses, so enter positive values for both answers.

(a)	τ A =	MPa
(b)	τ max =	MPa

y ty tw N d УА A bi

Answer 1

Complete solution is given below.

K 290 17T 140 10 406 mm 372 78 18€ 168 " Inertia 1> Moment of I 290* 406 12 e) - ( 2X 140X 372 12 Is 416.143 x 100 mm A & Shear stress at point Consider curea folow point A (Shaded arca) a = Ay (108 x 10) (1065) + (290x 17)(108+ SZ) KQ = 0.632665 X10mens

TA 11 210x103 x 0.632665X106 416,143 x 106 x 10 I b = 31.93 mpal 3) Maximum Shear stress CAt centroidal axis) > Consider area below centroidal asis. Q = Ay (186x10)(186) + (290x17) (186 +2) KQ = 11310'865 x 100 mm) Tmax 210x 103 x 1131.865 x103 416.143 x 106 x 10 VQ . I b Imaxe 57012 mpa