Bending Lab Report (Daniel Díaz, Harish & Jayanth)

Structural mechanics – Lab workStudy of bending and truss

MSc AME – Structural MechanicsDaniel Diaz, Jayanth & Harish

ISAE-ENSMA

Structural MechanicsDaniel Díaz, Jayanth & Harish

Study of bending

Introduction

The main goal of the experiments is the validation of the theorem of reciprocity (or Maxwell-Betti’s theorem). The set-up consists in a straight beam of length 4L clamped at point A and simply supported at C. Two loading cases are considered:

There will be two different parts of the study:

1) Theoretical study

Determine for each loading case:

- Case 1: reaction force Y1c at C, then deflection v1

B at B.

- Case 2: reaction for Y2c at C, then v2

D at D.

Instructions: Case 1 must be solved using energetic approach, namely Menabrea’s theorem and Castigliano`s theorem, ir order to calculate, reaction Y1

C and deflection v1B, respectively. Case 2 must be solved

using displacement’s approach.

This part has been done by hand and is attached in the next pages.

2) Experimental study: studied after the theoretical analysis.

2

ISAE-ENSMA


3

ISAE-ENSMA


4

ISAE-ENSMA


5

ISAE-ENSMA


6

ISAE-ENSMA


7

ISAE-ENSMA


8

ISAE-ENSMA


9

ISAE-ENSMA


Experimental study

Apply loads indicated in the measurement form in order to measure reaction force at C and deflection.

Introduce here the experiment results and measurements. Compare with theoretical results and explain differences.

10

ISAE-ENSMA


Study of a truss – Cremona method

Introduction

Consider the plane truss described below. Determine axial force in each bars using Cremona method (Cremona diagram should be clear enough to illustrate the method).

Dimensions are given in cm. The load P is equal to 3000 daN

Compare these results with those obtained using finite element method.

Bars are tubes made of steels (yield strength 200 MPa) of external diameter D (identical for the 6 bars) and of thickness e=6 mm. Determine the minimum value of D using a coefficient of safety of 2.

We have performed two ways of applying the Cremona method. The first one is just drawing the scheme to obtain the different values measuring the lines. The second one is done calculating all the angles and distances mathematically.

11

ISAE-ENSMA


Put here your scheme.

12

ISAE-ENSMA


13

ISAE-ENSMA


14

ISAE-ENSMA


15

ISAE-ENSMA


Put here the FEM results and compare with Cremona method.

16

Bending Lab Report (Daniel Díaz, Harish & Jayanth)

Documents

Transcript of Bending Lab Report (Daniel Díaz, Harish & Jayanth)