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Dear Mr. Khan,
Good Day.
I have two questions for you.
1. Suppose you have a non-linear simply supported beam. By non-linear I mean the beam span starts from the support say 4m then bends @ an angle of 40 Deg.(any angle less than 90)and span continues for additional say 3m to the next support. If this beam is supporting 6Tons/m, what is the approximate design forces(i.e. Torsion, Shear, and Moment(Manual approximate procedure))?
2. Say you have a R.C.Building composes of six or max. seven
Hi Mr. Jarkas,
Your second question is incomplete. Here is the answer to your first:
If the two supports are fully simply supported, then there will be no torsional resistance, and the cranked (non-linear, as you call it) beam will simply twist over sideways and end up sitting like an open-V (try it with a bent piece of wire!). However, if there is fixity at one end, or torsional fixity (which is practically very difficult to achieve without also having moment fixity), then the torsion at any point is the sum of the load times the eccentricity of that load from a straight line drawn between the supports. An approximate way of doing this is to break up the UDL into loads per metre section and multiply that by the eccentricity mentioned above.
The shear will be similar to as if the beam was straight, but taking account of the load over the actual lengths (i.e. 3+4 metres).
The moment diagram you can then work out from the shear, or reactions at each end, which are equal and of value (6X7)/2=21 tonnes, if both ends have the same type of support.(i.e. either simply supported or fixed)
I hope this is clear enough for you.
Kind regards,
Arshad Khan
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Answers by Expert:
Arshad Khan
Expertise
I can answer any questions to do with civil and structural engineering consultancy and construction industry in East Africa and the Middle East, and specifically with the analysis and design of reinforced concrete structures. My particular expertise is in the aseismic design and optimisation of tall buildings.
Experience
Employment history: 36 years in Construction and consultancy in the UK, Kenya, Tanzania, Uganda, Ethiopia, Eritrea, South Africa, Somalia, Zambia, Austria, Bahrain, Kuwait, Doha and the U.A.E.
Organizations
.Fellow of Institution of Structural Engineers (UK)
.Fellow of Institution of Civil Engineers(UK)
.Member of the Institution of Engineers, Kenya
.Registered Engineer, ERB, Kenya
.Member of the Architectural Association of Kenya (Engineers Chapter)
.Chartered Engineer (UK)
Publications
•1984: International Conference on the Art and Practice of Structural Design, London
•1994: 3rd Int. Kerensky Conference in Structural Engineering, Singapore
•2008: International Conference on High-Rise Towers, Abu Dhabi
Education/Credentials
BSc, 1st Class Hons, in Building Engineering, University of Bath, UK
MSc in Concrete Structures and Technology, University of London.
Diploma of Imperial College, UK.
Awards and Honors
•Science Congress Special Award (for 2-seater Hovercraft - 1968)
•Institution of Civil Engineers Award for outstanding performance at Bath University (1975)
•Concrete Society Postgraduate study Bursary Award (1976)
•Consular Representative for British High Commission, Nairobi. (1995 to 1998)
•Examiner for Institution of Civil Engineers Professional Interviews, Nairobi. (1997 to 1998)
•Branch Representative in Vienna for PI assessment for Inst. of Struct. Engrs. (1999 to date)
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