Question

Figure 1 shows A fully symmetrical I beam of area A1 = 5472 mm?, and second moment of areal = 59.9 x 10 mm' that is strengthened by attaching a plate of 10 mm thickness and 100 mm breadth at the top as shown in Figure 2. Pairs of 12 mm diameter steel bolts are used at regular 200 mm spacing along the beam to connect the plate to the I beam in an arrangement as shown in Figure 3. The compound beam is subject to a positive bending moment (M) of 26 kNm and a negative shearing force (S) of 50 kN. You do not need any other dimensions of the beam. Calculate: a) The location of the neutral axis of the compound beamy: b) The maximum compressive stress in the beam; c) The average shear stress in the bolts. d) The average bearing stress between the bolts and the 10 mm thick top plate

Answer 1

Solution:

If you found this solution useful then please upvote

for any query please comment

Thank you,.

Solution given, Ap=5472 mme, mmy 6 I = 59.9 X 109 t = 10 mm Shear Force, C5) = 50 KN I- beum in an → The beam to connect the plate to the arrangement as shown in the Figure. 14 100mm 키 ka *10mm T 280 min 9 positive bending moment (M) in c. c. 6. = 26 KN-m Negutive sheas Force i-e down words = 50 KN (4) Location of Neutral axis of compound beam: je j Alt J2A2 Alt A2 5 = 285 mm .: ý = 140 mm, z = 280+ to 2 A2= 100x10=1000 mm2 A = 5472 min 2 : = (140x 5472) + (285X 1000) 5472 +1000 ý= 162.404 mm

(6) maximum compressive stress in beam; Due to counter clock wise moment mux. Compressive stress occurs in top of the section. : 6= - mxy IN.A INA = II NA TIRNA - Where, y=distance from Neyteus Axis to the point of Application :: Y=290-7= 290- 162.404 = 127 596 mm NOW According to parallel Axis Theonem, FINA. = I, t A, ni? here, hi= ý- 140 = 162-404 - 140 = 22.404 may : Is N.A - 59.9x109+ (5472 x 22.404%) 626466 11. 39 mmt similarly, I2 N.A. = I2 + A2h2² h2= 42- I, =100x103 = 285 - 162.404 12 = 122.596 mm I2 N. A. = 100x103 + 1000x (122.5963) Ia N.A. = 15038112.55 mm му = .: Compressive stress, 6= - My I NA ILNA + TENA -

N :: 6=-26 X10' x 127.596 77684723.94 mm² (: 1 Nllamme 1 MPa) : 6 = .42-705 MPa Nature - Ve sign Represents Compressive (C) Average shear stress in the bolts :- I bort = 2X Tud? 50x103 - I bolt 2X † (12) 4 I bolt = 221.05 MP4 (d) Avenage begging stress between the bolt and plate (Iomm]: F 6 beaning Area (projected) 6 bearing 50 x103 12 x 10 x 10 416.67 MPa 6 begring Please upvote