Question

EXERCISE: BEAM FLEXURE #1 For the cantilever beam shown in the figure, find (a) the maximum bending stress and its location; and (b) the bending stress at a point 20 mm from the top of the beam on section B. -1.0 kN/m T A с 150 mm -2m- 6 m 50 mm #2 For the beam shown, calculate (a) the maximum bending stress; and (b) the bending stress at a point 0.5 in. from the top of the beam on section D. 2000 lb 3 ft 2 in. B D А E 4 in. 6 ft 6 ft

Please answer 1 and 2 with complete solution

Answer 1

#1 Mc 1 kN/m *B Reactions: & Fnzo, Carol ² fy=0) - {x1x 6+ (y=0. 2-m 6m G skilmi (y= 3 KN (11) A 2 m Бkt <Me =0, x1x6x (&) - Me=0 1Me=-6 kNm (2) B um FBD 3KN B MA=0 MB = -x + x2) x2 + 1 - 2 x 2) IMB = -2 kNm BMD 6kNm [Mc = -6 kNm Mman -6/KN.m (Absolute) moment of inestre (1) 50 (150) I = 3d? NA d=15oun 12 I = 14062500 munt b=soum

@ musi mkem bendery Sloess Oman Mnan Iman T Mman = 6 kNm = 6X166 N.mm (Hoggry moment) cc da Iman = = 180 10 - 75mm Oman (T) - Omas - RA 6X166x75 14662500 N/mm2 Toman=32 mpa Oman (c) Al support (C) Bendeng stress at somme from top at Point B' MB = 2 kNm = 2X10 € Nomm (Hogging) 9 OB= MB Le comm I 7812 dis 1 #1 YB = 9-20= 150 20 YB = 55mm 8B = (2/97X166 x 55 Ni minh 14062500 120mm 10B = 0.869/mpa 100 NA At pocut si

2 200 lb SMEO, BE A 3 B 3.0 Ay Ey Axx12-200x9=0 Ay = 150 lb Ety=0 Ay+ Eg-2020 Ey=200-150 [Ey = sols 450lbst Snold-St + BMD MA = ME=0 MB = A x 3 = 156 x3 = 450 lb ft MB = Ey x6 = 50 x6 = 300 lb ft {Mman = 450 fb st moment of inestia (I) 2 in I = 2143 _ 32 int 4 in 12 benelery stress mexemum mana Mman Iman Mmon - 450 lb-ft = 450X12 - 5400 is in (sagarry Iman = 1/2 = 2 in

Oman = 540x2 bibl2in2 32 Oman (C) Tmy man = - 1012.5 psi NA Suran (T) At Section 'BI © Bendery Stress at a point osin from top at sechon 'DI Mo = 300 ls. It = 3600 lb-in Y = 2-0.5=1.5 in lois lyo -.0 3600x1.5 32 3 Oo=506.250/Psi

Answer 2

Determine the max normal and shearing stresses for the cantilever beam showen below if the rectangular cross-section is (300*400) mm