Question

Problem 1.3. Shear stress distribution over the cross-section of a beam Figure 1.9 depicts a beam with a rectangular cross-section of a width and height h. This beam is subjected to a vertical shear force, V2, and the resulting shear stress distribution is assumed to be uniformly distributed over the cross-section, i.e., T12 V (h). (1) Is this assumption reasonable? Explain your answer. *Typo: V3 should be V2 Fig. 1.9. Uniform distribution of shear stresses over the cross-section of a beam.

Answer 1

Answer:

Given that:

A beam with a rectangular cross-section of a width b and height h.

Answer :- given thal- # sheni stress in Beams; m u uun az parabolic variation py Hot- нь - cross-sectional *-* section. -ASSUMP Hons- and flowing hook's law material is homogeneous, Isotropic - The generated shear stress is uniform along the width (constant Prom EF) st means shear stress will weigh along the depth Id' only shear stress the - Shear force is 'V' then the > 14 any section at any level EF is given by My - V.AY I b V = ar X-X section Applied shear force I - MOJ OF to Lal Area about NA. at level EF where shear b = width of the section Stress is required. A r Area either above cor) below the level ER centroidal distance of considered area prom NA. =

given Niz 11n Tiz : average shear stress in the beam T111 Ko + P rang we know Eman Ty = VAY Tь F16 I ready = bh3 12 s ry = v(ble-y). b [ 9+ 12 (512-9) -42 > Parabolic Varia bina ( 1103*- y2 parabolic variation - Y=0, Tylmal nmar = 6V x 2²/4 = 312 u/bh amar = 3 bh² Normal Javerage shear stress (Mavg for) M2 raug • Parg Pavo =v/bb |N10=v1bb k by :: teie vo=V and gaiven given av нь So V3 = ve it is resonable.