The deflection at the midpoint of a uniform beam of length l, flexural rigidity EI and weight per unit length w, subject to an axial force P, is where m 2 P EI On making the substitution 1 2ml, show that As the force P is relaxed, the deflection should reduce to that of a beam sagging under its own...

48 1 Setting 0 ml m and P 2 so d w 1 H 40 40 EI w4 Now sec 0 ...

The deflection at the midpoint of a uniform beam of length l, flexural rigidity EI and weight

Question:

The deflection at the midpoint of a uniform beam of length l, flexural rigidity EI and weight per unit length w, subject to an axial force P, is

W d = (sec-ml - 1) - mP wl 8P

where m² = P/EI. On making the substitution θ = 1/2ml, show that

d = wl 2 sec 02-0 32EI 04

As the force P is relaxed, the deflection should reduce to that of a beam sagging under its own weight. By first representing sec θ by its Maclaurin series expansion, show that

lim d = 00 5w14 384EI

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Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

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Question Posted: Jan 16, 2024 03:01 AM

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The deflection at the midpoint of a uniform beam of length l, flexural rigidity EI and weight

Question:

W d = (sec-ml - 1) - mP wl 8P

Step by Step Answer:

48 1 Setting 0 ml m and P 2 so d w 1 H 40 40 EI w4 Now sec 0 ...View the full answer

Modern Engineering Mathematics

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