Strength of materials(3) - PROBLEMS CHAPTER 5 Longitudinal...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
PROBLEMS CHAPTER 5 Longitudinal Strains in Beams 5.4-4 A cantilever beam AB is loaded by a couple M 0 at its free end (see figure). The length of the beam is L = 1.2 m and the longitudinal normal strain at the top surface is 0.0008. The distance from the top surface of the beam to the neutral surface is 50 mm. Calculate the radius of curvature ρ , the curvature κ , and the vertical deflection δ at the end of the beam. PROB. 5.4-4 Solution: (a) Curvature . () 1 50 1 1 62.5 0.016 0.0008 62.5 x ym m mm m ρκ ερ =− = = Negative signs mean the center of curvature is below the beam. (b) The vertical deflection then can be obtained. 1c o s 1.2 arcsin arcsin 1.10 62.5 m 62.5 1 cos 1.10 11.5 o o in which Lm δρ θ ρ == = ⎡⎤ ∴=− = ⎣⎦ m Negative signs means that the deflection is downward. Normal Stresses in Beams 5.5-4 A simply supported wood beam AB with span length L = 3.75 m carries a uniform load of intensity q = 6.4 kN/m (see figure). Calculate the maximum bending stress σ max due to the load q if the beam has a rectangular cross section with width b = 150 mm and height h = 300 mm. R A R B B PROB. 5.5-4
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Solution: (a) Reactions, shear forces and bending moments . () ( ) 11 6.4 . 3.75 12 22 AB R R qL kN m m kN == = × × = qL/ 2 qL 2 / 8 0 M 0 V - qL/ 2 ( ) 2 2 max 6.4 . 3.75 11.25 . 88 M qL kNm m × × = (b) Section modulus. 2 25 150 300 22.5 10 66 3 S bh mm mm mm × = × (c) Maximum bending stress. max max 53 11.25 . 5 M kN m MPa S mm σ = × 5.5-10 A fiberglass pipe is hoisted by a crane using a sling, as shown in the figure. The outer diameter of the pipe is 150 ram, its thickness is 6 mm, and its weight density is 18 kN/m 3 . The length of the pipe is L = 13 m and the distance between lifting points is s = 4 m. Determine the maximum bending stress in the pipe due to its own weight. PROB.5.5-10 Solution: (a) First plot the free-body diagram of the pipe. R A R B q s L A B
Background image of page 2
Load intensity or weight per unit length is () ( ) 22 3 18 / 150 150 2 6 48.86 / 4 kN m mm mm mm qN π ⎡⎤ ×− × ⎣⎦ == m Reactions at A and B are ( ) 11 48.86 . 13 317.6 AB RR q L N m m N = × × = (b) Shear forces and bending moments . -494.8Nm 0 M 0 V 97.7N 97.7N 219.9N -494.8Nm -379.1Nm 2 max 1 494.8 . 8 Mq L N m (c) Section modulus ( ) 44 64 43 150 150 2 6 7.048 10 64 9.40 10 150 / 2 I mm mm mm mm Im m Sm m cm m =− × = × × = × (d) Maximum bending stress. max max 494.8 . 5.26 M Nm MPa S mm σ = × Design of Beams 5.6 - 6 A pontoon bridge (see figure) is constructed of two longitudinal wood beams, known as balks , that span between adjacent pontoons and support the transverse floor beams, which are called chesses. For purposes of design, assume that a uniform floor load of 10 kPa acts over the chesses . (This load includes an allowance for the weights of the chesses and balks.) Also, assume that the chesses are 2.4 m long and that the balks are simply supported with a span of 3.6 m. The allowable bending stress in the wood is 17.5 MPa. If the balks have a square cross section, what is their minimum required width b min ?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
PROB, 5.6-6 Solution: (a) The load intensity on the two balks is () ( ) 10 2.4 24 / qk P a mk N = m (b) Consider the balks as a simply beam applied with uniform distributed load and the maximum bending moment in the beam is ( ) 2 2 max 11 24 / 3.6 38.9 88 Mq L k N m m k N == × × = m (c) Required section modulus then can be obtained.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/07/2011 for the course 3ME WB1114 taught by Professor I.paraschiv during the Spring '08 term at Technische Universiteit Delft.

Page1 / 17

Strength of materials(3) - PROBLEMS CHAPTER 5 Longitudinal...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online