MH các ND ôn tập SBVL

Determine the resultant internal normal force, shear force, and bending moment at point C in the beam 1, F1-4, page 16... Find the resultant internal loading acting on the cross sectio

MỘT SỐ BÀI TẬP MINH HỌA CHO 5 NỘI DUNG THI ĐÃ PHỔ BIẾN CHO SINH VIÊN

(Dạng liên kết, tải trọng, hình học mặt cắt ngang,… chỉ có tính tham khảo để minh họa

cho nội dung ôn tập)

January 8, 2021

I Internal force

Prob 1 Determine the resultant internal normal force, shear force, and bending moment at point C in the beam (1,

F1-4, page 16)

I Internal force

Prob 2 Find the resultant internal loading acting on the

cross section at point A ( P1-1, page 15)

Prob 3 The blade of the hacksaw is subjected to a pretension

force of F = 100 N

a) Determine the resultant internal loadings acting on section

a–a that passes through point D.

b) Determine the resultant internal loadings acting on section

b–b that passes through point D.

D

II Bending stress & Shear stress

Prob 1 The beam shown in Fig a has a cross-sectional

area in the shape of a channel, Fig b Determine the

maximum bending stress and shear stress that occurs in

the beam at section a–a ( Example 6.13, page 299)

Prob 2 If the beam is subjected to a moment of M = 100 kN.m and

a shear force Q = 40 kN

a) Determine the bending stress at points A, B, and C; sketch the

bending stress distribution on the cross section (P6-80, page

307)

b) Determine the maximum shear stress that occurs on the section

c) Determine equivalent stress at point D (using

maximum-distortion energy theory of failure – TB4).

III Strength verification & Deflection of a beam

Prob 3

a) Draw the shear and moment diagrams for the beam;

b) If d = 450 mm, determine the absolute maximum bending stress in the overhanging beam;

c) If the allowable bending stress is allow = 6 MPa, determine the minimum dimension d of the beam’s cross-sectional area to

the nearest mm (P6-100/101, page 309)

d) If the modulus of elasticity (Young’s modulus) is E, find the vertical displacement of point C and the rotational angle of

the section at C (Using Vereshchagin's rule).

C

III Strength verification & Deflection of a beam

Prob 2 Determine the displacement at point C EI is constant (P14-87, page 775)

(Using Vereshchagin's rule)

III Strength verification & Deflection of a beam

Prob 1.

a) Draw the shear and moment diagrams for the beam

b) Determine the minimum dimension b to the nearest mm of the beam’s cross section to safely support the load The wood

has an allowable normal stress of allow = 12 MPa and an allowable shear stress of allow = 1.5 MPa (F11-5, page 556)

b) Determine the displacement at point C as a function of b and EI (EI is constant)

C

IV Combined loading

Prob 1 The tubular shaft has an inner diameter of 15 mm Determine to the nearest millimeter its minimum outer diameter if

it is subjected to the gear loading The bearings at A and B exert force components only in the y and z directions on the shaft

a) Use an allowable shear stress of allow = [] = 70 MPa, and base the design on the maximum shear stress theory of failure

(TB3) (P11-39, page 589)

b) Use the maximum-distortion energy theory of failure (TB4) with allow = [] = 80 MPa

V Statically Indeterminate

Prob 1 Determine the reactions at the supports, then draw the shear and moment diagrams EI is constant (P12-118, page

674)

Prob 1 Determine the reactions at the supports, then draw the shear and moment diagrams EI is constant (P12-123, page

674)