CVG2140 Lecture 15 Shear Due to Bending 2in1 Color

1CVG2140 Winter 2014Mechanics of Materials

Course InstructorWon Taek Oh

A609(CBY)[email protected]

13 March 2014 Department of Civil Engineering

@(613)562-5800 Ext. 6687

Resultant Forces Produced by Bending Stress

2

(E1 = E2)

2 Resultant Forces Produced by Bending Stress

2 2 2 211 0 6000 2 0 6000212

BF . N mm / mm . N mm mm

kN

3

2 2 2 211 5 6000 3 0 60002

18

CF . N mm / mm . N mm mm

kN

Resultant Forces Produced by Bending Stress

Shear force

4

3 Example 1A beam segment if subjected to the internal bending moments shown. The cross-sectional dimensions of the beam are given. gDetermine the horizontal force required to satisfy equilibrium for the specified area and show the location and direction of this force in the sketch.

5

The Shear Stress Formula Shear stresses produced in a prismatic beam made of a

homogeneous liner-elastic material

6

4 The Shear Stress Formula Shear stresses produced in a prismatic beam made of a

homogeneous liner-elastic materialg

7

The Shear Stress Formula Shear stresses produced in a prismatic beam made of a

homogeneous liner-elastic material

0x HA Az z

M MMF y dA y dA FI I

0x HA A Az z z

M M MF y dA y dA y dA FI I I

M MF y dA y dA

8

H A Az z

F y dA y dAI I

H

z

MQFI

5 The Shear Stress Formula Shear stresses produced in a

prismatic beam made of a phomogeneous liner-elastic material

34

675 3000006

33750000H z

kN mm mmMQF kNI mm

9

The Shear Stress Formula Shear stress in a beam

,H

H avgz z

F M Q M Qt x t x I x I t

0x

10

Hz

dM Qdx I t

6 The Shear Stress Formula Shear stress in a beam

dM Vdx

Hz

VQI t

11

z

VQI t

Shear stress formula