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Helicoidal Stair.xls

Dr Youssef Hamida

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ABSTRACT: Current practice of analyzing free-standing stair slabs is to

use approximate analytical methods due to the absence of specific

code provisions

Because of their inherent limitations, these approaches cannot

predict the actual 3D behaviour of the stair slab system. Analytical methods cannot predict the distribution of any stress

resultants across any section. Such drawbacks of the analytical approaches manifest the

necessity of the development of a more rational but simple analysis

and design method With this objective, extensive numerical study

on the behaviour of the free-standing stair was made using thick

shell finite elements Stairs are essential features of all residential and commercial

buildings. From architectural point of view, free-standing stairs are more

attractive than ordinary ones.

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However, due to the lack of a simple rational design code,

designers are forced to make a conservative design resulting in a.n

unnecessarily heavy looking structure الطرق التقریبة استخدام ھو بذاتھ قائم حر درج بالطة لتصمیم الحالیة الممارسة

معین كود أحكام وجود لعدم نظرا التحلیلیة و

للنظام الفعلي 3D بسلوك التنبؤ یمكن ال األسالیب ھذه لھا، المالزمة القیود وبسبب•

.جزء أي في اإلجھاد محصالت أي بتوزیع تتنبأ ال التحلیل وطرق الدرج بالطة

نظر وجھة من والتجاریة السكنیة المباني لجمیع األساسیة السمات ھي الساللم•

العادیة تلك من جاذبیة أكثر ھي وال بذاتھا قائمةال والساللم المعماریة،

لجعل المصممین یضطر معقول، لتصمیم بسیط كود وجود لعدم نظرا ذلك، ومع•

لھ داعي ال ثقیال منظرا الى اعطارالشكل إلى أدى مما ا محافظ التصمیم

تقوم فكرة تصمیم وتحلبل الساللم على اعتبار االدراج الحرة مسنودة في الوسط عند البسطة

العزوم والفتل تورشن في ھذا وتصمم البالطة وفق االدراج العادیة في بتواجد مسند وھمیة

المسند الوھمي

ثم نسقط ردود الفعل على البالطات المائلة ویعاد تصمیمھا باضافة تسلیح قوى الشد والضغط

S= P/A على محاور البالطات ویصبح التصمیم خاضع الى االنعطاف المركب والتورشن

+_M*Y/I

The idea of the design and analysis of the stairs to consider of stairs

Free supporter in the center of the landing at the imaginary s supported

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and designed in accordance with the ordinary slab plate in moments

and torsion at this imaginary support S= P/A +_M*Y/I

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under the loads N are, for any two adjacent slabs AB and BC, calculated from formula (2) in Table 178, in which MAB

and are found from formula (1) if the structure is freely

supported at the end of L.

For each pair of slabs AB—BC, etc. there is an equation like (2) containing three unknown forces F.

If there are n pairs, there are (n — 1)

equations and (n + 1) unknowns. The conditions at the outer edges a and z of the end slabs determine the forces F at

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these edges; for example, if the edges are unsupported, Fa F0 = 0. The simultaneous equations are solved for the remaining unknown forces FA, F8, etc.

The longitudinal stress at any junction B is calculated from the formula (in Table 178) for f8.

Variation of the longitudinal stress from one function to the next is rectilinear.

If fB is negative, the stress is tensile and should be resisted by reinforcement. Shearing stresses are generally small

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Helical stairs

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Example.

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میثال

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References:

Dr wahib zid aldean

Charles E. Reynolds BSc (Eng), CEng, FICE

and James C. Steedman

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Dr Youssef hamida