Question

A simply support beam is loaded as shown in the following figure. 1) Draw the shear force and bending moment diagrams. 2) Calculate the maximum bending stress in the beam. 3) Calculate the maximum shear stress in the beam. G0 KN 30 kNm B0 kN/m H NA 0.1 m 3 m e 1.5m to 1.5m. 0.1 m

Answer 1

Gogo 30 kNm SOKNim 3m B (1.5m) C (1.5m) 4 - Looko - 200KN 200 SRD (KN) - - 100 - Vmax=+200 KN 40 2150 (+) 240 190 30KNM BMD (KNM) Mmax= 250 kium 21ррорт Reactor Axro Ex=0 Ey=0, Ay+ Oy - 80x3 +60 = 300 -0 ZMAZO BOA'T Dy Y6 +30 - 60x 4.5 - 80x3x1.520 > Dy= 100 kN A Ay = 200 kN.

collcolation For SFD and BRD Shear Force Coup) ↑ It It Ill I sign convention moment (Mo) CL+ (-D T Tome AB oca c3m, xyoom A V x = 200 - 800 - - (Linear) Var 200 KN. & Vo = - 40kn location of vaso on 200-800 » 0 = 2.5m moment Mac 2003- 8032 - - - MB - XN2O xxm + 240KN.M Cdx=2.5m Ma 250 KN.m .... max moment in AB TDC ozal1.5m x 4oom D x = -100 -.-- (constant) Maa Loox + 30 - - - Lénear MA= 30kNm & Me= 180kNm TEBI 1.520 L 3m x 4oom D Va= - 100+60 -- 40 kN - - constant - Lineam Mas +1000+30-60 (X-1.5) MB - 240 KN.nn

# Shear Stress Distribution Tin Beams + T - SCAT) - f ТЬ Where A Y & mom Section of area a-a of about above section N.A, Z at a distance 'yo & Shear stress from NA b e wiath of 'Y' of rom Section NA at a distance e - Shear flow y from N.A. at any (KN/m) distance 9 SF at Section - Xay I 10.1 of total as about N.A. C to

omaa 1.5X10KN/m I haoim y=0.050 30000 kN/m Tmas O.imab omar Bending stocs Shear stress elefan clist? Benolong stress ror Rectangular Oma Memas = mch ) INA = 0.1*0.13 12 250x100, 0.05 = 10.4 (0.14 T2 loma 1500000 = 1.5810 KN/m2 stress occur at N.A. Shear stress mar shear NAT e v= mas s.r. AY= moment of Aroca about NA In 200x10.05x0.17 0.057 09** 0.4 b= width (mar = 30000 kN/m2 1